Chapter 6: Polynomials and Polynomial Functions
(Additional Practice – page 947-948)
FDCSD Standards & Benchmarks
M2: Understands and applies basic and advanced properties of the concept of numbers
M2.36 Identify and graph functions and relations.
M3: Uses basic and advanced procedures while performing the process of computation.
M3.37 Solves problems involving radicals, exponents, and logarithms
M8: Understands and applies basic and advanced properties of functions and algebra.
M8.28 Uses appropriate terminology and notation to define functions and their
properties
M8.33 Compares and applies the numerical, symbolic, and graphical properties of a
variety of functions
M8.34 Uses a variety of algebraic and graphical methods to solve polynomial sentences
with real and complex roots
M8.37 Identifies and analyzes linear and nonlinear patterns in data using line graphs
M8.39 Represents problems using algebraic functions and graphs of those functions
Simplify the following expressions.
43)
45)
(
23 x 2
x !1y
xy !2
)
5
=
= 215 x10
44)
y3
46)
x2
x 11y 10
x y
!3
!1
=
x14y11
y 10 20x 14 20x 14y 10
!
=
= 10x10y 4
3
6
4 6
2x
xy
2x y
Factor completely:
2x 7 ! 32x 3
(
(x
)
! 4) ( x
2x 3 x 4 ! 16
47) 2x 3
2
2
+4
)
48)
( )( )
(x
) (
)
x ( x ! 4) + 4 ( x ! 4)
3
! 4x 2 + 4x ! 16
2
( )
"
%
2x3 x-2 x+2 $ x2+4'
#
&
" 2 %
$# x +4'& x-4
- 11 -
Created 12/08
x 4 + 10x 2 + 16
x3 ! 8
49) x 3 ! 23
50)
( x-2)"$# x2+2x+4%'&
! 2 $! 2 $
#" x +8&% #" x +2&%
51) x 3 ! 12x 2 + 12x + 80 , given 10 is a zero
1 !12 12 80
10 !20 !80
10 1 !2 !8
0
(x ! 10) (x
2
! 2x ! 8
)
( x-10)( x-4)( x+2)
Find the roots of the following functions.
()
52) f x = 16x 4 + 54
()
53) f x = 3x 3 ! 2x 2 ! 9x + 6
3x 3 ! 2x 2 ! 9x + 6 = 0
(3x ! 2x ) + (!9x + 6) = 0
x (3x ! 2) ! 3 (3x ! 2) = 0
(x ! 3) (3x ! 2) = 0
3
16x 4 + 54 = 0
16x 4 = !54
27
x4 = !
8
2
2
x = ± 3 or x =
no real zeroes
54)
2
2
3
" 3,0$ ," - 3,0$ ," 2,0$
#
% #
% &# 3 '%
55)
(-1,0),(3,0),(1,0),(1,0)
(-3,0),(-1,0),(0,0),(1,0),(3,0)
- 12 -
Created 12/08
Divide
55)
(6x
2
) (
)
+ x + 7 ÷ 2x + 3
56)
(2x
4
) (
+ 2x 3 ! 10x ! 9 ÷ x 3 + x 2 ! 5
3x ! 4
2x
2x + 3 6x 2 + x + 7
(
! 6x 2 + 9x
)
(
x + x ! 5 2x + 2x ! 10x ! 9
3
! 8x + 7
2
3x-4+
57)
(x
2
3
2x-
19
2x+3
) (
)
3
(
)
! 7x ! 6 ÷ x ! 2
4
! 2x 4 + 2x 3 ! 10x
! !8x ! 12
19
)
58)
( 4x
4
)
!9
9
x3+x2-5
) (
+ 5x 3 + 2x 2 ! 1 ÷ x + 1
1
0
!7
!6
4
1
2
2
4 !6
!3 !12
!1 4
5
!4
1
2
!1
1
0
!1
!1
)
!1
1
0
4x3+x2+x-1
12
x2+2x-3x-2
- 13 -
Created 12/08