#(!04%2
£{
-œṎœ˜ÃÊiÞ
0OLYNOMIALS
!2% 9/5 2%!$9 0!'% LIKE TERMS
COEFFICIENT
!SSOCIATIVE 0ROPERTY
$ISTRIBUTIVE 0ROPERTY
$IVIDE THE FIGURE INTO FOUR RECTANGLES
! LW
2ECTANGLE ! q S D q UNITS 2ECTANGLE ! q UNITS 2ECTANGLE ! S D q q UNITS 2ECTANGLE ! S D q q UNITS 4OTAL AREA UNITS S D S D S D q !REA OF LARGE RECTANGLE
! LW
! q FT !REA OF SMALL RECTANGLE
! LW
! S D q S D q FT !REA OF SHADED PORTION !REA OF LARGE RECTANGLE !REA OF SMALL RECTANGLE FT
q X q X X q X X X q Y q Y Y Y Z q Z Z Z A q A A q A A A B q B B q B B 0!'%3 n
S D q q 4HINK AND $ISCUSS
S X Y D X Y
0OSSIBLE ANSWER 9OU CAN CLASSIFY A POLYNOMIAL
BY THE NUMBER OF TERMS AND BY THE DEGREE 4HE
POLYNOMIAL X X IS A TRINOMIAL WITH A
DEGREE OF S A B D A B
S R S D R S
! LW
! q CM 0OSSIBLE ANSWER X IS A DIFFERENCE OF
MONOMIALS 4HE EXPONENT OF X IS NOT A
WHOLE NUMBER
!REA OF RECTANGLE
! LW
! q IN !REA OF TRIANGLE
! ??BH
! ?? S D S D ?? S D IN !REA OF SHADED PORTION !REA OF RECTANGLE !REA OF TRIANGLE IN %XERCISES
X Y
9ES IT IS A MONOMIAL
???
X
NOT A MONOMIAL ! MONOMIAL CANNOT HAVE A VARIABLE
IN THE DENOMINATOR
!REA OF LARGE RECTANGLE
! LW
! q M !REA OF SMALL RECTANGLE
! LW
! q M !REA OF SHADED PORTION !REA OF LARGE RECTANGLE !REA OF SMALL RECTANGLE M ,ET X BE THE BASE OF ONE TRIANGLE AND X BE
THE BASE OF THE OTHER TRIANGLE &IND THE AREA OF EACH
TRIANGLE
! ??BH
! ?? S X D S D X
! ??BH
! ?? S X D S D S X D X
4OTAL AREA X X FT #OPYRIGHT © BY (OLT -C$OUGAL
!LL RIGHTS RESERVED
^
q X NOT A MONOMIAL #ANNOT TAKE THE SQUARE ROOT OF A
VARIABLE IN A MONOMIAL
9ES IT IS A MONOMIAL
??X Y
BINOMIAL
R R TRINOMIAL
X
??
X
NOT A POLYNOMIAL ! POLYNOMIAL CANNOT HAVE A
VARIABLE IN THE DENOMINATOR
MONOMIAL
(OLT -C$OUGAL -ATHEMATICS
M M $EGREE $EGREE 4HE DEGREE OF M M IS X
$EGREE $EGREE 4HE DEGREE OF X IS $EGREE 4HE DEGREE OF IS T T S D S D 4HE BALLS HEIGHT AFTER SECONDS IS FEET
X NOT A MONOMIAL ! MONOMIAL CANNOT HAVE A
NEGATIVE EXPONENT
Y ???
X
NOT A MONOMIAL ! MONOMIAL CANNOT HAVE A VARIABLE
IN THE DENOMINATOR
??X Y MONOMIAL
X
NOT A MONOMIAL 4HE EXPONENT IS A VARIABLE NOT A
WHOLE NUMBER
M N MONOMIAL
??
G H NOT A POLYNOMIAL ?? IS NOT A WHOLE NUMBER
X X TRINOMIAL
A BINOMIAL
q^
X
NOT A POLYNOMIAL CANNOT TAKE THE SQUARE ROOT OF
THE VARIABLE
V S
MONOMIAL
M
M
$EGREE $EGREE $EGREE 4HE DEGREE OF M M IS #OPYRIGHT © BY (OLT -C$OUGAL
!LL RIGHTS RESERVED
P P $EGREE $EGREE 4HE DEGREE OF P P IS N
$EGREE $EGREE 4HE DEGREE OF N IS Y $EGREE 4HE DEGREE OF Y IS R R
???
?????
????
FT
)T WILL TAKE APPROXIMATELY FT FOR THE CAR TO STOP
X MONOMIAL DEGREE X X
NOT A POLYNOMIAL -UST HAVE WHOLE NUMBER
EXPONENT
??X ??X BINOMIAL DEGREE Y Y
BINOMIAL DEGREE F F F
TRINOMIAL DEGREE ?
?
X
NOT A POLYNOMIAL NO VARIABLES IN THE DENOMINATOR
X q^
X
NOT A POLYNOMIAL NO SQUARE ROOTS OF THE VARIABLES
X NOT A POLYNOMIAL NOT A WHOLE NUMBER EXPONENT
B B B TRINOMIAL DEGREE X
BINOMIAL DEGREE ??
X X
$EGREE $EGREE $EGREE 4HE DEGREE OF X X IS X
X $EGREE $EGREE $EGREE 4HE DEGREE OF X X IS X X X
S D S D S D
IN X MONOMIAL
MONOMIAL
X X NOT A POLYNOMIAL EXPONENT NOT A WHOLE NUMBER
MONOMIAL DEGREE (OLT -C$OUGAL -ATHEMATICS
S S S S D S D MIGAL
S S D S D MIGAL
S S D S D MIGAL
S S S S D S D MIGAL
S S D S D MIGAL
S S D S D MIGAL
S S S S D S D MIGAL
S S D S D MIGAL
S S D S D MIGAL
" X HAS THE GREATEST VALUE WHEN X )F YOU
NOTICE ALL OF THE BINOMIALS ARE EXACTLY THE SAME
WITH THE EXCEPTION OF THE EXPONENT OF THE VARIABLE X
4HEREFORE THE BINOMIAL WITH THE GREATEST VALUE IS
THE ONE WHOSE DEGREE IS THE HIGHEST
0OSSIBLE ANSWER 4HE STUDENT NEEDS TO LOOK AT
ALL THREE TERMS OF THE POLYNOMIAL TO DETERMINE THE
DEGREE NOT JUST THE DEGREE OF THE FIRST TERM 4HE
DEGREE IS B X H X X ! ??BH
! ?? S X D S X X D
)F X ! ?? S D S q q D
?
! ? S D S D
! ?? S D S D
! UNITS * T VT S
S D S D S D FT *
K K DEGREE X X X X ???
???
X J J
J
?
J
J
??
???
J
J
?
M M
M
M
?
?
M
??????
???????
M
M 0!'%3 n
4HINK AND $ISCUSS
0OSSIBLE ANSWER 4HE TERMS ARE EITHER NUMBERS OR
TERMS WITH THE SAME VARIABLES RAISED TO THE SAME
POWERS AND THEY ARE SEPARATED BY PLUS OR MINUS
SIGNS
0OSSIBLE ANSWER S X D X X X X
%XERCISES
B B B B
,IKE TERMS B AND B B AND B
0OSSIBLE ANSWER MONORAIL BICYCLE TRIPOD POLYGON
! MONORAIL HAS ONE RAIL FOR A TRACK AND A MONOMIAL
HAS ONE TERM ! BICYCLE HAS TWO WHEELS AND A
BINOMIAL HAS TWO TERMS ! TRIPOD HAS THREE LEGS
AND A TRINOMIAL HAS THREE TERMS ! POLYGON CAN
HAVE MANY SIDES AND A POLYNOMIAL CAN HAVE
MANY TERMS
#OPYRIGHT © BY (OLT -C$OUGAL
!LL RIGHTS RESERVED
MN M N M N M N
,IKE TERMS M N AND M N X X X X X X X X X X X X X X (OLT -C$OUGAL -ATHEMATICS
B B B B B B B B B B B B B B B B B B S X D
S M M D S M M D
M M M M
M M
S X X D
S X X D
q X q X
X X
S A A D A A
S A A D A A
q A q A A A
A A A A
A A
X S X D
X q X q X
X X
T T T T ,IKE TERMS T AND T T AND T RS R S R S RS ,IKE TERMS RS AND RS R S AND R S P P P P P P P P P P FG F G FG FG F G FG FG F G FG FG F G FG
F G FG S X X D X X
q X q X X X
X X X X
X X
S B D B B q B q B B B B B B B ?? S Y D Y ?? q Y ?? q Y Y Y Y S H H H D
q H q H q H H H H H H H
S S S S S S #OPYRIGHT © BY (OLT -C$OUGAL
!LL RIGHTS RESERVED
S X X D X X X X X X S X X X D X
X X X X
X X X
S X D
q X q X GH G H G H G H
GH G H
B B S B D
B B B B B MN M N S M N MN D
MN M N M N MN
MN
S X Y D S X Y D
X Y X Y
X Y
S D D
D A 6 S S S S S DS S ,ET S 6 S D 4HE VOLUME OF THE SCULPTURE IS CM B 3 S S S S S DS S ,ET S 3 S D 4HE SURFACE AREA OF THE SCULPTURE IS CM 4HE SURFACE AREA IS EQUAL TO THE SUM OF THE AREAS
OF THE INNER LATERAL SURFACE THE OUTER LATERAL SURFACE
AND THE TWO BASES
XY XY Y Y
S DXY S DY
XY Y IN 6 QXY QXY S Q QDXY QXY ,ET X AND Y 6 Q S D S D Q IN y 4HE VOLUME OF THE RING IS ABOUT IN # X X X X
X X X
X X X X 4HE LIKE TERMS ARE hX AND X v AND hX AND X v
3IMPLIFIED X X (OLT -C$OUGAL -ATHEMATICS
????
X
???
2%!$9 4/ '/ /. 0!'% q X
X
????
?????
X
X ???
X NOT A MONOMIAL ! MONOMIAL CANNOT HAVE A VARIABLE
IN THE DENOMINATOR
??X X NOT A MONOMIAL ! MONOMIAL HAS ONLY TERM
????
X
????
q X
X
?????
??????
X
X C D MONOMIAL
?
?
XX
NOT A POLYNOMIAL ! POLYNOMIAL CANNOT HAVE A
VARIABLE IN THE DENOMINATOR
X
F TX E X A A TRINOMIAL
S D S D Y BINOMIAL
S D S D S D S D U
$EGREE $EGREE 4HE DEGREE OF U IS C C
C
$EGREE $EGREE $EGREE $EGREE 4HE DEGREE OF C C C IS $EGREE 4HE DEGREE OF IS S D Y
%VALUATE Y Y Y FOR Y S D S D S D 4HE DEPTH OF THE SUBMARINE AFTER MINUTES IS FT
X
X
F TX E X X S D S D S D S D S D S D S D S D S D S D S D S D S D S D #OPYRIGHT © BY (OLT -C$OUGAL
!LL RIGHTS RESERVED
X Y XY X Y
,IKE TERMS X Y AND X Y Z Z Z Z ,IKE TERMS Z AND Z Z AND Z
T T ,IKE TERMS T AND T AND AB AC BC AC AB
,IKE TERMS AB AND AB AC AND AC
B B B B B B B S DB S D
B B Y Y Y Y Y Y Y Y S DY S DY Y Y S X X D X X
X X X X
X X X X
S DX S DX
X X
(OLT -C$OUGAL -ATHEMATICS
Y Y S Y D
Y Y Y Y Y Y S DY S D
Y 0 S W D S W D S W D S W D
W W W W
W IN
S X Y XY D S XY X Y D
X Y XY XY X Y
X Y XY 4HE AREA OF EACH FACE OF THE CUBE IS S S
! CUBE HAS FACES SO THE TOTAL SURFACE AREA OF
THE CUBE IS S S S D S S
S G D S G G D
G G G G G 4HE AREA OF EACH LATERAL FACE OF A REGULAR SQUARE
PYRAMID IS ??B B ! LATERAL FACE IS A FACE THAT IS
NOT THE BASE ! REGULAR SQUARE PYRAMID HAS FACES
THAT ARE NOT THE BASE SO THE TOTAL LATERAL SURFACE
AREA IS ??B B B B
S
BC B C BC BC BC S BC B C BC D S BC BC D
BC B C BC D
S H H H D S H H H D
H H H H H H H H H
0!'%3 n
4HINK AND $ISCUSS
0OSSIBLE ANSWER 4O ADD HORIZONTALLY YOU APPLY THE
#OMMUTATIVE AND !SSOCIATIVE 0ROPERTIES TO REORDER
AND REGROUP THE TERMS 4O ADD VERTICALLY YOU LINE UP
THE LIKE TERMS IN COLUMNS
0OSSIBLE ANSWER )T IS AN APPLICATION OF THE
!SSOCIATIVE 0ROPERTY OF !DDITION
%XERCISES
S T T D S T T D
T T T T ??
T T S B C B C BC D S B C BC D
S B C BC D
B C B C BC
B C BC B C BC ???
B C B C BC S X X D S X D
X X X X X S X D S X D
X X X S W W D S W W D W W W W W W W W ??
W W S R S RS D S R S RS D S R S RS D
R S RS R S RS R S RS
R S RS
S B B D S B B D
B B B B ??
B B %QUILATERAL TRIANGLE
LW
0 L
SW D
W 3QUARE
L S W D
0 L
S W D
W 0ERIMETER OF EQUILATERAL TRIANGLE AND SQUARE
S W D S W D
W UNITS
S AB AB A B D S AB A B D
AB A B AB AB A B
AB A B AB
A B ???
AB AB A B S H J HJ HJ D S HJ D S H J HJ D
H J HJ HJ HJ H J
HJ
H J HJ HJ 4HE LENGTH OF MATERIAL #OLETTE NEEDS EQUALS THE
PERIMETER OF THE OUTSIDE OF THE FRAME $RAW A
DIAGRAM TO HELP YOU DETERMINE THE OUTER DIMENSIONS
OF THE FRAME
"ASE W W W W
W
(EIGHT W W W W
W
#OPYRIGHT © BY (OLT -C$OUGAL
!LL RIGHTS RESERVED
S PQ P Q PQ D S P Q PQ D S PQ PQ P Q D
PQ P Q PQ P Q PQ PQ PQ P Q
PQ P Q
S W Y WY WY D S WY WY W Y D S WY WY W Y D
W Y WY WY WY WY W Y WY WY W Y
W Y WY WY
S P T PT D S P T PT PT D S PT P T D
P T PT P T PT PT PT P T
P T PT PT (OLT -C$OUGAL -ATHEMATICS
3PHERE
6 ??QR ?? S DR y R #UBE
6 R
0RISM
6 R R R 3UM OF 6OLUMES
y S R D S R D S R R R D
y R R R R R y R R R # 0OOL LENGTH W W
0OOL WIDTH W W
0 S W W D S W W D
S W W D S W W D
W W W W W W W W
W
#OST OF PRODUCTION
N N #OST OF PACKAGING
N N 4OTAL COST S N N D S N N D
N N N N N N 0OSSIBLE ANSWER !DD THE EXPRESSION REPRESENTING
THE DISTANCE FROM THE AIRPORT TO THE FIRST PLANE TO
THE EXPRESSION REPRESENTING THE DISTANCE FROM THE
AIRPORT TO THE SECOND PLANE
S X X D S X X D X X X X X X 4HE PLANES ARE X X MILES APART AFTER
HOURS
0OSSIBLE ANSWER S M M D S M M D
# S X X D S X U D X X X U X
X
X
?
?
U X
4HE MISSING TERM IS X
0OSSIBLE ANSWER (OW FAR APART WILL THE PLANES BE
AFTER HOURS
SX D SX D X X X 4HE PLANES WILL BE X MILES APART AFTER
HOURS
0OSSIBLE ANSWER &IRST IDENTIFY LIKE TERMS 4HEN ADD
LIKE TERMS BY ADDING THEIR COEFFICIENTS
S X X D S UX UX U D X X &IRST FIND THE X TERM
X U X X X ?
?
U X &IND THE XTERM
X U X
X
X
?
?
U X
&IND THE CONSTANTTERM
U ?
?
U 4HE POLYNOMIAL IS X X #OPYRIGHT © BY (OLT -C$OUGAL
!LL RIGHTS RESERVED
S X X X D S X X X D
S X X X D X X X X X X X X X 4HE SUM IS !LL OF THE OTHER TERMS DROP OUT
INCHES ?????
INCH
????????
X FEET
FEET
q X q X FT
INCHES ?????
INCH
?????????
X FEET
FEET
q X q X FT
INCHES
INCH
???????
?????
X FEET
FEET
qXq
X FT
INCHES
INCH
?????????
?????
X FEET
FEET
q X q X FT
???
???
OR ????
???
???
????
?? ????
0!'%3 n
4HINK AND $ISCUSS
0OSSIBLE ANSWER #HANGE THE SIGN OF EVERY TERM IN
THE POLYNOMIAL TO ITS OPPOSITE
0OSSIBLE ANSWER 4O SUBTRACT A POLYNOMIAL YOU FIRST
CHANGE THE POLYNOMIAL THAT IS BEING SUBTRACTED TO ITS
OPPOSITE AND THEN YOU ADD
%XERCISES
X Y
S X Y D
X Y
X XY S X XY D
X XY X X S X X D
X X Y Y S Y Y D
Y Y (OLT -C$OUGAL -ATHEMATICS
X X S X X D
X X S X X D
X X S X X D O ??
X
X ??
X X XY Y S XY Y D
XY Y S A B AB A D
S
A B A B D O
???
A B AB A
A B A B ???
A B AB A B S B B D S B B D
S B B D S B B D
B B B B B B B B S B B D
B S B B D
B B B B B P P T PT P P T PT ???
P P P T PT T T T S T T T D
T T T S T T T D
T T T T T T T T T AMPERES
S M N MN MN D S MN M N D
S M N MN MN D S MN M N D
M N MN MN MN M N
M N MN MN
S X X D
X X S X X D O X X ??
??
X X S X Y XY X D
X Y XY X S XY X D O XY X ??
??
X Y XY X S AB AB A B D
S AB AB A B D O
???
6OLUME OF LARGER RECTANGULAR PRISM 6OLUME OF
SMALLER RECTANGULAR PRISM
S X X X D S X X X D
S X X X D S X X X D
X X X X X X X X X IN RN S RN D
RN V V S V V D
V V M M S M M D
M M XY XY
S XY XY D
XY XY
N N N
S N N N D
N N N
B B S B B D
B B S Y Y D S Y Y D
S Y Y D S Y Y D
Y Y Y Y Y DOLLARS
" S X X D HAS THE GREATEST VALUE 4HE
STRATEGY IS TO LOOK AT THE VALUE OF THE EXPONENTS 4HE
GREATER THE EXPONENT THE LARGER THE RESULT WHEN
IS RAISED TO THAT POWER BUT YOU ALSO HAVE TO LOOK
AT THE SIGNS 4HE SIGNS WILL MAKE THE VALUE OF
THE POLYNOMIAL GREATER /PTION " HAS A PRETTY LARGE
EXPONENT AS WELL AS ADDITION SIGNS THROUGHOUT
S A A D S A A D
S A A D S A A D
A A A A
A S R S RS R S RS D S RS R S RS D
S R S RS R S RS D S RS R S RS D
R S RS R S RS RS R S RS
R S RS R S RS
#OPYRIGHT © BY (OLT -C$OUGAL
!LL RIGHTS RESERVED
S PQ P Q PQ D S PQ P Q PQ D
S PQ P Q PQ D S PQ P Q PQ D
PQ P Q PQ PQ P Q PQ
PQ P Q PQ
,ET ! BE THE AREA OF THE SHADED REGION
! !REA OF RECTANGLE !REA OF SQUARE
S A A D S A A D
S A A D S A A D
A A A A A A CM ,ET ! BE THE AREA OF THE SHADED REGION
! !REA OF SQUARE !REA OF TRIANGLE
S X X D S X X D
S X X D S X X D
X X X X X X IN S W W D S W W D
S W W D S W W D
W W W W W W S A B AB D S A B AB D
S A B AB D S A B AB D
A B AB A B AB
B AB
S Y X Y X D S Y X Y X D
S Y X Y X D S Y X Y X D
Y X Y X Y X Y X Y X Y X AB A B AB
AB A B AB ???
AB A B AB S PT P P T D
??
S P PT P T D
0OSSIBLE ANSWER &IND THE OPPOSITE OF X X AND ADD IT TO X X 4HE RESULT IS X X
(OLT -C$OUGAL -ATHEMATICS
S T AT BT D S CT T T D T T T D
S T AT BT D S CT T T D T T T D
T AT BT CT T T T T T D
3OLVE FOR C THE COEFFICIENT OF T T CT T S C DT C ?
?
C q C q C 3OLVE FOR A THE COEFFICIENT OF T AT T T S A DT T A ?
?
A q A q A
3OLVE FOR B THE COEFFICIENT OF T
BT T T
S B DT T
B ?
?
B B ???
????
B
3OLVE FOR D THE CONSTANT
D
D
4HE VALUES OF A B C AND D ARE A B C D * S A B AB AB D S A B AB AB D
S X X D S X D
S X X D S X D
X X X X FOR X S D UNITS ^
q ^
q ^
q ^
q X Y X Y X Y X Y X Y
S ZY ZY D ZY ZY ZY ZY ZY ZY ZY ZY
S X X D
X X 0!'%3 n
4HINK AND $ISCUSS
0OSSIBLE ANSWER 4O MULTIPLY TWO MONOMIALS
MULTIPLY THE COEFFICIENTS AND ADD EXPONENTS
OF POWERS WITH THE SAME BASES 4O MULTIPLY A
POLYNOMIAL BY A MONOMIAL APPLY THE $ISTRIBUTIVE
0ROPERTY AND MULTIPLY THE RESULTING MONOMIALS
#OPYRIGHT © BY (OLT -C$OUGAL
!LL RIGHTS RESERVED
%XERCISES
S S T DS ST D
q q S q T S T S X Y DS X Y D
q q X q Y X Y S H J D S H F D
q q H q J H J M S M D
q q M M P R S PR D
q q P q R P R G H S G H D
q q G q H G H H S M H D
HM H AB S A B AB D
A B A B X S X X D
X X X
C D S CD C D CD D
C D C D C D ,ET H BE THE HEIGHT OF THE TRAPEZOID AND LET B AND
B BE THE LENGTHS OF ITS BASES 4HE AREA OF THE
TRAPEZOID IS ! ??H S B B D 5SE THE $ISTRIBUTIVE
0ROPERTY TO WRITE THIS EXPRESSION ANOTHER WAY
! ??H S B B D
?
! ?B H ??B H
?
?
! q q ?? q q ! IN S X Y DS XY D
X Y
S GH DS G H D
G H S A B DS B D
A B X Y ??X Y
X Y S S T D S ST D
S T S
D
J S H J D
H J S M N DS MN D
M N M N Z S Z Z D
Z Z H S H H D
H H CD S C D CD D
C D C D B S B B D
B B B
S T S S T ST S T D
S T S T S T
(OLT -C$OUGAL -ATHEMATICS
4HE BASE B OF THE RECTANGLE IS X Y AND THE HEIGHT
H IS X XY 4HE AREA OF THE RECTANGLE IS
! BH X Y S X XY D 5SE THE
$ISTRIBUTIVE 0ROPERTY TO WRITE THIS EXPRESSION
ANOTHER WAY
! X Y S X XY D
X Y X Y X Y
,ET X AND Y ! S D S D S DS D S D S D
S D S D S D S D S D S D
UNITS S B DS B D
B S M N DS MN D
M N S A B DS AB D
A B G S G D
G G
M S M M D
M M AB S A B AB D
A B A B X S X X Y D
X X Y M S X D
MX M
F G F G F G F G F G X S X X D
X X X S M P DS M P MP M P D
M P M P M P WZ S W Z WZ W Z D
W Z W Z W Z 4HE HEIGHT OF THE CYLINDER IS X Y 4HE VOLUME OF
THE CYLINDER 6 QR H
6 QR S X Y D
QR X QR Y ,ET R ?? X AND AND Y 6 Q ?? S D Q ?? S D Q Q Q FT
S D
S D
A P S A D P PA
P S A D P PA
??P S A D P ??PA
??P S A D P ??PA
-ALE
.ONATHLETIC
P PA
&IT
P ??PA
S
S
D S
D S
&EMALE
P PA
P ??PA
D
B P ??PA P ??PA
?
?
P PA P ??PA
?
?
?
?
P PA P PA
P
#OPYRIGHT © BY (OLT -C$OUGAL
!LL RIGHTS RESERVED
D
0OSSIBLE ANSWERS 7HAT IS THE VOLUME OF THE PRISM
IN CUBIC UNITS 7HAT IS THE SURFACE AREA OF THE
PRISM IN SQUARE UNITS
4HE NUMBER OF TERMS IN THE ANSWER IS THE SAME AS
THE NUMBER OF TERMS IN THE POLYNOMIAL 4HE DEGREE
OF THE ANSWER IS THE DEGREE OF THE POLYNOMIAL PLUS
THE DEGREE OF THE MONOMIAL
3IMPLIFY P S P P D P S P D P P P P P P P P P P 0GUESSING TWO OR MORE CORRECTLY 0GUESSING
FEWER THAN TWO CORRECTLY 0GUESSING FEWER THAN TWO CORRECTLY
0GUESSING TWO OR MORE CORRECTLY
S P P P D
S P P P D
P P P ! !REA OF RECTANGLE LW
WIDTH OF THIS RECTANGLE L ! L S L D
! L L
L L
L L S L D S L D L OR L L ?? OR L 4HE LENGTH CANNOT BE NEGATIVE SO THE LENGTH FT
4HE WIDTH L S D FT
! ??BH
! ?? S CD DS C D CD D
S CD DS C D CD D
C D C D WHEN C AND D S D S D S D S D UNITS 3URFACE AREA OF A RECTANGULAR PRISM LW LH WH
3! LW LH WH
S q D S q D S q D
IN 3URFACE AREA OF A CYLINDER QRH QR 3! QRH QR S q q q D S q q S D D
CM XY A
XY A
S D A
S D A A ?
?
Y ?A
Y ?A
X
X
Y ???
Y ???
X
X
XY A
S D A ?
Y ?A
X
Y ???
X
(OLT -C$OUGAL -ATHEMATICS
0!'%3 n
S W D S W D
S X D S X D
SW D SW D
S X D S X D
W W W W W X X X X X 4HINK AND $ISCUSS
TERMS
S A B D S C D D AC AD BC BD
TERMS
S X D S X D X X TERMS
SX D SX D X S M D S M D
S B C D S B C D
S M D S M D
S B C D S B C D
M M M M M B BC BC C B BC C %XERCISES
S X D S Y D
S X D S X D
SX D SY D
SX D SX D
XY X Y X X X X X S T D S T D
S R S D S R S D
S T D S T D
S R S D S R S D
T T T T T S N B D S N B D
S M D S M D
S M D S M D
S N B D S N B D
M M M M M S H D S H D
S M D S M D
S H D S H D
SM D SM D
H H H H H M M M M M N BN BN B N BN B 4HE TOTAL AREA AREA OF POOL WITH THE DECK ADDED
4HE DIMENSIONS OF THE POOL ITSELF ARE YD YD
4HE DIMENSIONS OF THE POOL WITH ADDED DECK ARE
S X D S X D
S B C D S B C D
S X D S X D S B C D S B C D
X X X X X YD B BC BC C B BC C S X D !REA OF 7ALKWAY 4OTAL !REA !REA OF #OURTYARD
S X D S X D S D S D
X X X X X FT S X D
SX D SX D
X X X X X S X D SB D SB D
B B B B X X X X X X X X X X S X D S X D
S V D S V D
SX D SX D
SV D SV D
X X X X X V V V V V SX D SX D
SB D SB D
X X X X X B B B B B S X D S X D
SX D SX D
S X D S X D
X X X X S X D S X D S X D S X D
S B D S X D S X D
S B D S B D
SX D SX D
#OPYRIGHT © BY (OLT -C$OUGAL
!LL RIGHTS RESERVED
R RS RS S R RS S X X X X S A D S X D S X D
SA D SA D
X X X X X A A A A A S M D S M D
M M M M S B D S B D
B B B B B S Q DS Q D
Q Q Q Q Q S T D S T D
T T T T T (OLT -C$OUGAL -ATHEMATICS
S Q D S Q DS Q D
Q Q Q Q Q IN MODEL IN OBJECT
OR ???
?? OR CM MODEL CM OBJECT
OR ???
?? OR IN MODEL FT IN OBJECT
FT IN IN
OR ???
OR ???
CM MODEL CM OBJECT
OR ???
OR ???
S M M D
M M S R S D S R S D
R RS RS S R RS S S A B A AB D AB
A B A AB AB
A B A AB
4HE PIECE OF TIN IS IN BY IN AND A SQUARE
WITH SIDE LENGTH X IS CUT OUT OF EACH CORNER
,ENGTH OF BASE X
,ENGTH OF WIDTH X
!REA OF BASE
! S X D S X D
X X X X X IN X Y S XY X Y XY D
X Y XY X Y XY
X Y XY XY
S G DS G D
G G G G S B D S B D
B B B B B S T D S T D
T T T T T S M N D S M N D
M MN MN N M MN N S A B D S A B D S A B D
A AB AB B A AB B S R D S R D
R R R R 2%!$9 4/ '/ /. 0!'% S X X D S X D
X X X X X S0 A D S6 B D C
06 B0 A6 AB C
S X D S X D
X X X ,ET - BE THE MAXIMUM FORCE 3O 0 - AND A ??-
S0 A D S6 B D C
S B C B C BC D S B C BC D S B C BC D
B C B C BC B C BC B C BC B C B C BC S- ??- D S6 B D C
??- S 6 B D C
??-6 ??-B C
0OSSIBLE ANSWER !S 0 INCREASES 6 DECREASES AND
AS 6 INCREASES 0 DECREASES
S W W D S W W D S W D
W W W W W W W S 0 A D S 6 B D C
S0 A D S6 B D
C
?????????????
?????
6B
6B
C
0 A ?????
6B
C A
0 ?????
6B
" S X D S X D
X X X 4HE &/), METHOD IS USED IN OPTION "
X X X 0ERIMETER OF EQUILATERAL TRIANGLE
SW D SW D SW D
WWW
W 0ERIMETER OF SQUARE
S W D S W D S W D S W D
W W W W W 3UM OF THE PERIMETERS
S W D S W D
W W W M M X XY S M M D
S X XY D
M M X XY S A B D S A B D
A AB AB B A AB B 4HE COEFFICIENT OF AB IS #OPYRIGHT © BY (OLT -C$OUGAL
!LL RIGHTS RESERVED
(OLT -C$OUGAL -ATHEMATICS
V V S V V D
V V T T TRINOMIAL
R R NOT A POLYNOMIAL A POLYNOMIAL CANNOT HAVE
NEGATIVE EXPONENTS
G G ???
G
NOT A POLYNOMIAL A POLYNOMIAL CANNOT HAVE A
VARIABLE IN THE DENOMINATOR
B S B B D
B S B B D
B B B B B S A A D S A A D
A A S A A D
A A A A
A A S X
X X X A B C MONOMIAL
X D S X X D
X S X X D
X X X
X
C D S CD C D CD D
C D C D C D S T S S T ST S T D
S T S T S T ?? S X Y DS X XY D
?? S X Y X Y X Y D
X Y X Y X Y
S D S D S D S D S D S D
S X D S X D
X X X X X S X D SX D SX D
X X X X X S X D S X D
S X D S X D
X X X X X X X X $IMENSIONS OF RUG
S X D S X D
X X X X X FT #(!04%2 345$9 '5)$% 2%6)%7
0!'%3 n
POLYNOMIAL DEGREE OF POLYNOMIAL
&/), BINOMIALS
BINOMIAL TRINOMIAL
#OPYRIGHT © BY (OLT -C$OUGAL
!LL RIGHTS RESERVED
X X
X $EGREE $EGREE $EGREE 4HE DEGREE OF X X X IS X
X X
$EGREE $EGREE $EGREE $EGREE 4HE DEGREE OF X X X IS R R $EGREE $EGREE $EGREE 4HE DEGREE OF R R IS ?? M $EGREE $EGREE 4HE DEGREE OF ?? M ?? M ?? M IS X X
X
$EGREE $EGREE $EGREE 4HE DEGREE OF X X X IS ?? M $EGREE ?? M T T T T T T T T T T T T GH G H GH G H
S M D S M D
M M M M M S N D S N D
N N N N N S S T D S ST D
S T S HJ DS H J D
H J ^
q XY NOT A POLYNOMIAL A POLYNOMIAL CANNOT CONTAIN
SQUARE ROOTS
ST S BINOMIAL
S H H H D S H H H D
S H H H D S H H H D
H H H H H H H H H
S X Y DS XY D
X Y ^
qX GH G H GH G H
GH G H
S MN M D
MN M
MN M
S A B D B
A B B
A B B
A B
S ST T D ST T
ST T ST T
ST T ST T
ST T
S X X D S X X D
X X X X X X S X X X D S X X D
X X X X X X X X (OLT -C$OUGAL -ATHEMATICS
S H D S H D S H D
H H H H H S XY X Y XY D S X Y XY XY D
XY X Y XY X Y XY XY XY X Y XY
S N D S N D S N D
N N N
N S X D S X D
X S X D
X X X S W W D S W W D
W W S W W D
W W W W W W X Y S X Y X Y XY XY D
X Y S X Y X Y XY XY D
X Y X Y X Y X Y S X D S X D
S X D ?????????????????
X
X
??????????????
S X D
??????
S X D X
S X D S X D
X X CM S D S D CM S
S
S
D
S P DS P D
S P DS P D
P P P P P S X X D S X X D
X X S X X D
X X X X X X S B D S B D
S AB AB A B D S A B AB D
AB AB A B S A B AB D
AB AB A B A B AB
AB AB A B
S R D S R D
S P Q P Q D S PQ P Q D
P Q P Q S PQ P Q D
P Q P Q PQ P Q P Q P Q PQ B B B B B S R D S R D
R R R R R S A B D S A B D
S N N D S N N D
N N N N N N 4HE REMAINING AREA HAS AN AREA OF
N N CM S ST D S S ST D
S A B D S A B D
A AB AB B A AB B S M D S ST D S S ST D
S T S T ST SM
S T D S T D
S T D S T D
M S M M D
M S M M D
M M M
H S GH G H H G D
D SM D
M M M M M A B S A B AB A B D
A B S A B AB A B D
A B A B A B A B T T T T S B T D S B T D
S B T D S B T D
H S GH G H H G D
GH G H H GH
B BT BT T B BT T ?? J K S J K JK J K D
S X D S X D
?? J K S J K JK J K D
S X D S X D
J K ?? J K J K J K ?? J K J K #OPYRIGHT © BY (OLT -C$OUGAL
!LL RIGHTS RESERVED
D
D
X X X X X (OLT -C$OUGAL -ATHEMATICS
S H H H D S H H H D
H H H H H H H H H H H
S Y D S Y DS Y D
Y Y Y Y Y X S X D S X D
X S X X X D
X S X X D
X X X 4HE VOLUME OF THE BOX IS X X X IN #(!04%2 4%34 0!'% T T NOT A POLYNOMIAL IS NOT A WHOLE NUMBER
??A B MONOMIAL
M M TRINOMIAL
B M B
M $EGREE $EGREE $EGREE 4HE DEGREE OF B M IS $EGREE 4HE DEGREE OF IS S B C B C BC D S B C BC D
S B C BC D
B C B C BC B C BC B C BC B C B C BC ,ENGTH OF PORTRAIT WITH MAT S W D
7IDTH OF PORTRAIT WITH MAT S W D
0ERIMETER OF PORTRAIT WITH MAT
0 S W D S W D S W D S W D
S W D
W W
4HE PERIMETER OF THE OUTER EDGE OF THE MAT IS
W IN
S M N MN MN D S MN M N D
S M N MN MN D S MN M N D
M N MN MN MN M N
MN MN S A A D S A A D
S A A D S A A D
A A A A
A S A B A B AB D S A B A B D
S A B A B AB D S A B A B D
A B A B AB A B A B
A B A B AB Y
Y
$EGREE $EGREE 4HE DEGREE OF Y IS 6OLUME OF CUBE WITH SIDE LENGTH X IS
6 X X X S D S D S D CUBIC UNITS
A B B A B
A B
S X X D
X X S J J J D S J J J D
S J J J D S J J J D
J J J J J J J J J J !REA OF THE REMAINING PIECE OF PLYWOOD AREA OF
RECTANGLE AREA OF CIRCLE
S X X D S X X D
S X X D S X X D
X X X X X 4HE AREA OF THE REMAINING PIECE OF PLYWOOD IS
X UNITS X Y XY X Y X Y
X Y XY S X D S X D
X S X Y DS XY D
X Y S B B D B B
B B B B
B B
S A B D S A B D
A B A S A A D
A A A
4HE AREA OF ONE FACE OF A CUBE IS S S
4HE TOTAL SURFACE AREA OF THE CUBE
3! S S S D S S
S X X D S X D
X X X X S X D S X D
X X X S BC B C BC D S BC BC D
BC B C BC BC BC
BC B C BC #OPYRIGHT © BY (OLT -C$OUGAL
!LL RIGHTS RESERVED
M N S M N M N D
M N M N A S AB AB A D S X D S X D
A B A B A X X X X X S X D S X D
S A D S A D
X X X A A A X X A A ,ENGTH OF BASE OF FOLDED BOX X
7IDTH OF BASE OF FOLDED BOX X
!REA OF BASE OF FOLDED BOX ! S X D S X D
X X X X X IN (OLT -C$OUGAL -ATHEMATICS