10/6/11
5.6 Solving Polynomial Equations by
Factoring.
Use the Zero-Factor Property to solve equations.
Solve quadratic equations by factoring.
Solve higher-degree polynomial equations by factoring.
Quad ratic equations
are equations that can be written in the form
ax2
where a
≠
+
bx + c
=
0
0.
7
10/6/11
~
~
~
Solving quadratic equations
Strategy #1: FACTOR
Examples:
x2 +2x÷1=O
~-
~:~u~*$;~.
~
~
Solving quadratic equations
~Strategy #1: FACTOR
• Examples:
x2+1=2
zc,
=0
Ft
S
10/6/11
Solving quadratic equations
Strategy #1: FACTOR
Examples:
+
2x2
%a(2)
—
x
—
2
=
0
±
(‘÷i) ~
~*
_
Solve the equations
—13z+36=--z2
2
-
(~9
~
)(%_t\)
0
t~
m2 —8m+18=2
n_\t_Bcfl
4.%4~ tO
=0
\~=~
9
10/6/11
Solve the equations
(x~ +2x37(9x2 —18x)=0
~c3(%~2) ~(-9~)(%#I)to
/
7__~
t2) .=o
I
/1
3u3
=
5u2 + 2u
Solve the equations
1-(x÷1)2 =0
-
(\
—~c—~)(
-~
—
~*~c#~)
(nl)c5
6x2
+
x —6
=
0
10
10/6/11
One more
(z+6)(z+3)=4
a
~
~
(~
2
492 +\~*~0
#1
)(~
42)
~t-2
Word problem
II]
4[t~
‘The outside dimensions of a picture frame are 28
centimeters and 20 centimeters. The area of the exposed
part of the picture is 468 square centimeters. Find the
width w of the picture frame.
-u
28
(is- 2,)(202)c)
0~~
=
—‘1
20
0
If
U]
~9~O—
2’hc+’~c~’
—
z~j]
2~% +QSto
~~(—
~)
* 23
2S_2L23) 4c~
11
tO
10/6/11
Garden Problem revisited...
I want to put a fence around my garden to keep the dogs
out. To make it easy on myself I’ll make it rectangular I
bought 60 yards of lattice fence, and I want to use all of
it. And, I want the yard to have area of 250 square yard.
Can it be done?
Atl(rao
19.4 ~ L00
tn
(so
30 tA)
2So
-
~
LV
2-So
/4~~
co~cktc
2~ I2iS
12