Algebra II Pre AP
Name __
Date
Notes & WS 8.5 B - Dividing Polynomials
~
--c--
.
-.
.Theorem
~-----.
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4.......L..~-----11f----- __
Example:
= X4 -
Given P(x)
If you divide a polynomial p(x) of degree n 2: 1 by x - a, then the
remainder is p(a)- -.
-~~
-~----~
~~ ~~----~~
2X2 - X + 122, what is P(3)?
P(3) is the remainder
By the Remainder Theorem,
-,-
when you divide
P(x) by x - 3.
~
Use synthetic division and the Remainder Theorem to find P( a) .
3J
+ 2x + 1, find P(3).
a,
-/2-
S
.3
S
P
P(3)
EX 2) PIx) = 2x3
-
0 -2
-1
122
a
9
21
60
3
7
20
1:2
= 182_
4x2 + 3x - 6, find P(
33
((
34
2-13 ).
(3) :::3'f
Use synthetic division and the given factor to completely factor the polynomial function.
function.
EX 3)
1
f
t:(
IS'
_
.....-~-
The Remainder Theorem
EX 1) PIx) = Sx3 -12x2
---
Period
j(x)=2x3+3x2-9x-l0;
.f ()d::=
:::J.l
Then sketch the graph of the
(x+l)
(X·...,) (Z-x+S)(x-:z.)
z
'3
-9 -to
-{
-2.-
~ )( 2.+ 3C
( 2~
0
-fO
I
~
/0
-I 0
+ S ) ()(
- 2.)
EX 4) The expression V(x) = x3 - 13x + 12 represents the volume of a rectangular safe in cubic feet. The length of the safe is
x + 4. What linear expressions with integer coefficients could represent the other dimensions of the safe?
~'fI....
(Assume that the height is greater than the width.)
o
- c.f
I
-13
+«:
f2.,.
.J.J" - / 2-
-4
3
-= ()(3
3 )(x
EXS) Use synthetic division to divide P(x)=9x -18x-12
G"-
Whatisthequotient?
~1< - I~
b)
Is 9x+6
'-11..0
-
"~X+IV
'h:+- c.
V'~,
1C-.3
-I)
by 9x+6.
J;q
-:lC3-,l..~-11
• ~-"
:t' +- ~
-'3f
a factor ofP(x)?
~"4'
I
~~3-laK-/2.
-<.J
~-I
~
0
)(2-_ L/ 't +- 3
a)
)(-I-~
01
I
io
I
0
-2..
-%
4/q
- ~
- (~
jt2._ ~
')l -
-"6
Zo/V
-
1'14 -
8Ji 7
~7
it +~.3
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