Math 1050-004
Worksheet
Meeting 20
The following pages contain practice problems and information for Basics of
Polynomials. You should work on them quietly while exams are being
returned.
Name: ___________________________________________ Number:
______________
Polynomial Addition
Example: If p(x) = 2x3 + 4x
using the following procedure:
1 and q(x)
=
—x3 + 5x2 + 2 then p(x) + q(x) can be found
-
-~
#sxt ~ Dr
=
3*s~z
1. If p(x)
=
+4t#\
4x2 + 5x + 1 and q(x)
lOx3 + 2, find p(x) + q(x).
‘1
[Ox~ ~
+O~
4- (Lf~i~o’)ct
-4-(S-i-b
-~-
3
Example: If p(x) 2x3 + 4x
using the following procedure:
—
Cx)-
1 and q(x)
—
=
—x3 + 5z2 + 2 then p(x)
~
(x)=
—
q(x) can be found
o~ ~
+
-
(z_ L-O)~c3 ÷
~ (q- D~x
-3
2. If p(x)
=
4x2 + 5x + 1 and q(x)
=
—lOx3 + 2, find p(x)
q(x).
±
-
[1ox~+cz2~ox ta]
Q-( ao))x3÷
-
(~v)~2
lox3 +q)ct +S~c
Page 2
+
-
~ (i a)
Polynomial Multiplication
3. If pQc)
5xt and q(z) =
2x + 1, use the distributive law to find their product
(p~zfl(q(x)) = (5x2)(x4 2x + 1). What is the leading term of the resulting polynomial?
—
—
—
~
(s~)(~9)÷ (~x~)(-l~)
~_
(sxj(I~
)D~ tS~
L€odjy1-terpyr 5x~
4 If p(x) = x3 + 4 and q(x) =
x, use the distributive property to find their product.
What is the leading term of the resulting polynomial?
—
)z
(x~t4)(x~-%)
x3(x2~)
t~(~L%)
flj÷(x3)(~)+ 9(~O+ 9(-~)
=
Fact: If p(x) and q(x) are polynomials, the leading term of their product p(x)q(z) is the
product of their leading terms. For example, (5x2)(x4) = 5x6, and (x3)(x2) = x5 in the two
problems above.
Page 3
5. Find the quotient using long division.
19 ~58~I3
—5’,
Ib&
—
92
—ii
—7-0
-hz
I
Page 4