PERIOD
DATE
NAME
The Remainder and Factor Theorems
Use s5rnthetic Bubstitution to frnd
fl-B)
and fl4) for each function.
l.f\x)=x2*?ac+3
Z.flx):x2-5r*10
8.f@)=x2-5x-4
a.f@)=tcg-x2-?ac+3
6.f(x)
=.nB
+
?.x2
+
5
7.f@)=icl-chz-?,tc+8
9.f(*)=13*3x2+zrc-50
?nz
l6.f(r) = x5 *'lxs -
4x
-
6x2
8.f(x) =
10./(r)
lL.f(*)=x4-%2-x+7
13.f(*) = 2*a - xs +
6.f(x) =,x3 -
:
Lz.f(x) =
:
+
%,
tcB
-
xz
+ 4x - 4
rc4
*
xs
-
2x4
-
Txz
3r3
+
- x + L2
4n2
-
?* +
t
- 43ca * 3x2 - 5r - 3
L6.f(x) = x6 * ch| - x4 + x3 - 9x2 + 20
26
L4.
- \0
f(*)
}xa
Given a pol5rnomial and one of its factors, frnd the remainirrg factors of the
polynomial.
L7.xa*3x2-6x-8;x-2
18.*3*7x2*7x-15;r-1
19.13-9x2*27x-27;x-3
2O.x3-tcz*8x+L2;tc+3
o
o
E
=.
@
f
@
a
o
22.x3-x2-L x+24;x*4
21..x3*5x2-%*24;r-2
5
o
o
o
o
=
o
E
23.3xi
-
tcz
-
L7x
*
6; x
+
{
?A.Atca-L%cz-x*3;x-B
2
=oo
@.
25. LSxs
*
9x2
-
?ac
* t; ?'x + L
o
26.6x3*5x2-Bx-2;3x-2
=
o
+
=
@
o
=
27.x5
Ag.
*
xa
-
1xs
-
5x2
+ 4x + 4;r
*
1
28.x5
-
2x4
+
4,*3
-
8x2
-
5x
*
o
LO;
x
-
2
pOpULAfION The projected population in thousands for a city over the next several
years can be estimated by the function P(x) = xs + ?a2 - 8r * 520, *here r is the
number of years since 2005. Use synthetic substitution to estimate the population
for 2010.
30.VOLUME The volume of water in a rectangular swimming pool can be modeled by the
polynomial 2tcs - 9x2 + 7x * 6.If the depth of the pool is given by the polynomial
2x + L, what polynomials express the length and width of the pool?
Chapter 6
38
Glencoe Algebra 2
ts
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