Polynomials Test Review Name:
Work out answers on another sheet of paper. This review is the day of the test and will be a quiz grade. No work = No credit.
Use long division or synthetic division to determine whether or not the given expression is a factor of the polynomial. Write out the resulting answer.
1.
x
3
+ x
2
+ 6x + 6; x + 1
2.
2x
3
– 6x
2
+ 2x – 14; 2x
2
– 7
3.
64x
3
– 8; 4x – 3
4.
-4x
3
+ 8x
2
+ 252x; x + 7
5.
x
3
+ 343; x
2
– 7x + 49
Factor, find the zeros, and describe the end behavior. Graph the odd problems on graph paper.
6.
y = 64x 3 – 8
7.
y = 2x
3
– 20x
2
+ 18x
8.
y = - 8x
4
+ 8x
3
+ 27x – 27
9.
y = x
4
+ 12x
3
+35x
2
– 12x – 36
10.
y = x
4
+ 13x
2
– 48
11.
y = - 10x 4 + 27x 3 – 25x 2 + 9x – 1
12.
y = x
6
– x
4
- 81x
2
+ 81
13.
y = 6x
5
– 17x
4
– 2x
3
+ 24x
2
– 4x – 7
14.
y = - 4x
4
+ 27x
2
+ 21x – 2
Find the inverse of each of the following functions, and graph both the original function and its inverse on graph paper.
15.
y = 4x
2
– 8x – 60 16.
y = 2x
2
+ 12x – 4 17.
y = (x + 3)
3
– 9
Suppose the following are zeroes for a polynomial. Find the equation of the polynomial with these zeroes that has a leading coefficient of 1.
18.
3 + i, 4, 1
19.
2 – 3 , -2, 2

Given the following data, find the polynomial equation that best fits the data.
20.
( 1, -2) (2, 7) (3, 18) (4, 31) (5, 46) (6, 63)
21.
(-1 -48) (0, -50) (1, -36) (2, 0) (3, 64) (4, 162)
Solve the following:
22.
You are in charge of making a container to hold a number of small candies. You may use one 3 in. x 5 in. index card to create a box. Find the dimensions of the box that maximize the number of candies you get and the maximum volume.
Graph:
23.
y
 
3 x

7

5
24.
y
 
2 3
 x

4
Solve the following for x:
25.
x

1
 x

7
26.
27.
x

3

2 x

9
 x

3 x

1

Rationalize or simplify x

4
28.
3 x y
8
6 xy
1
2 z
0
29.
3 x
1
2 y
3
4
30.
5
486
8

Polynomials Test Review Key
1.
Yes,
2.
No, x x
2 

3

6
9 x
2 x
2

35

7
3.
No, 16 x
2 
12 x
 
19
9
4 x

3
4.
5.
Yes,
Yes,
 x
4
 x
2 
36
7
6.
8 ( 2 x

1 )( 4 x
2  x
2 x
7.
2 x ( x

9 )( x

1 )

1 )
; as x
; as x
 
, f(x)
 
, as x
 
, f(x)
 
 
, f(x)
 
, as x
 
, f(x)
 
8.
–
( x
9.
( x

1 )( 2 x

1 )( x

3 )( 4 x
2

1 )( x

6 )
2

6 x

9 ) ; as x
 
, f(x)
 
, as x
 
, f(x)
 
; as x
 
, f(x)
 
, as x
 
, f(x)
 
10.
( x
2
11.

( x

3 )( x
2 
16 ) ; as x
 
, f(x)
 
, as x
 
, f(x)
 

1 )
2
( 5 x

1 )( 2 x

1 ) ; as x
 
, f(x)
 
, as x
 
, f(x)
 
12.
( x
13.
( x

3 )( x

1 )( x

1 )( x

1 )
2
( x

1 )( 3 x


3 )( x
2
7 )( 2 x

1 )

9 ) ; as x
 
, f(x)
 
, as x
 
, f(x)
 
; as x
 
, f(x)
 
, as x
 
, f(x)
 
14.
– ( x

1 )( x

2 )( 4 x
2 
12 x

1 ) ; as x
 
, f(x)
 
, as x
 
, f(x)
 
15.
y

1

1
2 x

64
16.
y
 
3
 x

22
2
17.
y
21.
y

3 x

9
 x
3 
8 x
2

3
18.
19.
20.
x
4 x
4 y


11 x
3

4 x
3 

44
3 x
2 x

2 x
2 
6 x

9

74
16 x
 x
4

40

5 x

50
22.
h = .6 in, length = 3.8 in, width = 1.8 in; max volume: approx 4.1 cubic inches
23.
see graphs
24.
see graphs
25.
x = 10
26.
no solution
27.
x = 0
28.
3 xy y
3
29.
2 x
1
2 y
1
4
30.
3 5
2
8

Graphs:
7)
9)
11)

13)
15) original: inverse:
16) original: inverse:

17) original: inverse:
23)
24)