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Math 3 - Polynomials Unit Review

Total questions: 48

Worksheet time: 2hrs 15mins

Name
Class
Date
1.
Classify by degree of polynomial:
3x3 – 6x
a)
Constant
b)
Linear
c)
Quadratic
d)
Cubic
2.
Classify by degree of polynomial:
2x – 9
a)
Constant
b)
Linear
c)
Quadratic
d)
Cubic
3.
Classify by degree of polynomial:
12
a)
Constant
b)
Linear
c)
Quadratic
d)
Cubic
4.
Classify by degree of polynomial:
-2x2 – x
a)
Constant
b)
Linear
c)
Quadratic
d)
Cubic
5.
What is the remainder of  (3x3 -5x2 -4x +1) ÷ (x + 3)?
a)
-25
b)
25
c)
113
d)
-113
6.
What is the standard form of the polynomial,
 9x2 + 5x + 27 + 2x3
a)
27 + 5x + 9x2 + 2x3
b)
9x2 + 5x + 2x3 + 27
c)
9x2 + 5x + 27 + 2x3
d)
2x3 + 9x2 + 5x + 27
7.

What is the leading coefficient of this polynomial?


4x3+2x2−1

a)

2

b)

−1

c)

Not written

d)

4

8.

What is the constant in this polynomial?

x2+4x+5

a)

1

b)

0

c)

5

d)

4

9.
What is the degree of the function graphed here?
a)
2
b)
3
c)
4
d)
5
10.
Is the leading coefficient positive or negative
a)
positive
b)
negative
11.
How many real solutions does the function have?
a)
0
b)
1
c)
2
d)
3
12.
Which function is graphed?
a)
(x - 4)(x + 2)(x - 8)=0
b)
(x - 4)(x - 2)(x + 8)=0
c)
(x - 4)(x + 2)(x + 8)=0
d)
(x + 4)(x + 2)(x + 8)=0
13.
What is the degree and end behaviors of the function behind this text? (As x−>∞, as x−>-∞, as usual...)
a)
2; ∞,-∞
b)
3; ∞,∞
c)
4; ∞,∞
d)
6; ∞,∞
14.
In the above graph complete the following end behavior:
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____
a)
-∞
-∞
b)
+∞
-∞
c)
-∞
+∞
d)
+∞
+∞
15.
The polynomial is...
a)
Odd degree, positive leading coefficient.
b)
Odd degree, negative leading coefficient.
c)
Even degree, positive leading coefficient.
d)
Even degree, negative leading coefficient.
16.
What are the
zeros of the polynomial
y = 3(x + 4)(x + 1)(x - 3)?
a)
-4, -1, 3
b)
3, -3, 4, 1
c)
4, 1, -3
d)
3, -4, -1, 3
17.
Describe the end behavior of
f(x) = -5x4 - 2x2 + 8
a)
Left side: Rises  
 Right side: Rises
b)
Left Side:  Rises
Right side: Falls
c)
Left side: Falls
Right side: Rises
d)
Left side: Falls
Right side: Falls
18.
Match the graph to the function
a)
f(x)= -x2+3x+2
b)
f(x) = -x3+2
c)
f(x) = x3+2
d)
f(x) = ⅓x⁴-5x²+2
19.
Match the graph to the function
a)
f(x) = -x⁴-x³+5x²-6
b)
f(x) = x⁴+3x²-3x+1
c)
f(x) = -x³+2x²-x-6
d)
f(x) = x⁴+x³+5x²-6
20.
What is the maximum(s) and minimum(s) values of the function behind this text?
a)
Minimum(s): 1; Maximum(s): 2
b)
Maximum(s): .5; Minimum(s): -5,-2
c)
Maximum(s): -.5; Minimum(s): -5,-2
d)
Maximum(s): -.5; Minimum(s): -5
21.
The function f(x)=2x6-3x4+2x-10 could...
a)
have 6 real zeros.
b)
have 6 turns.
c)
have 4 real zeros and 3 imaginary zeros.
d)
have ends that point in opposite directions.
22.
What is the domain of the graph?
a)
{x| -∞ ≤ x ≤ ∞}
b)
(-∞,∞)
c)
-3 ≤ x ≤ 3
d)
-15 ≤ y ≤ 9
23.
What is the range of the graph?
a)
-15 < y < ∞
b)
(-∞, ∞)
c)
(-15, ∞)
d)
[-15, ∞)
24.
What is the domain of the function?
a)
(-∞,∞)
b)
(-3.333, -2)
c)
(-∞, -2)
d)
(-3.333, ∞)
25.
What is another way to say "where a function crosses the x-axis"?
a)
x-intercept
b)
zero
c)
root
d)
all of these.
26.
What are the roots of the polynomial function?
y = (x + 2)(x - 7)3
a)
-2, 7 multiplicity 3
b)
-2, 7, 3
c)
2, -7 multiplicity 3
d)
2, -7, 3
27.
State the zeros of the polynomial (include multiplicity):
f(x) = x(x+3)2(x - 2)
a)
x = 0, 3, 2
b)
x = 0, -3 (multiplicity of 2), 2
c)
-3, 2
d)
0, 2 (multiplicity of 3)
28.
f(x)= x2(x – 2)3(x – 7)

Find and select each real zero and its multiplicity
a)
0 (Mult of 2), 2 (Mult of 3), 7 (mult 1)
b)
2 (Mult of 3), 7 (mult 1)
c)
0, 2, 7
d)
2 (mult of 2), 7 (mult of 3)
29.

Write the polynomial in standard form given the following zeros. x = -2, 1, 4

a)

f(x) = (x+2)(x-1)(x-4)

b)

f(x) =x3 - 3x2 - 6x + 8

c)

f(x) = x3 + 8

d)

f(x) = x3 - 3x2 + 8

30.

Write a polynomial in factored form with zeros at x = 1, x = -1 x = 0

a)

(x - 1)(x + 1)

b)

x(x - 1)(x + 1)

c)

x2(x - 1)(x + 1)

d)

x(x - 1)(x - 1)

31.
A polynomial function with rational coefficients has the follow zeros: -1 + i and √5 . Find all additional zeros.
a)
1 + i
b)
-√5 and 1 - i
c)
-√5 and -1 - i
d)
-1 - i
32.
Given x=5, x =3/2, and x= 5/3...
which of the following is the correct factored form? 
a)
(x-5)(2x-3)(3x-5)
b)
(x+5)(2x+3)(3x-5)
c)
(x-5)(x-3/2)(x-5/3)
d)
(x-5)(3x-2)(5x-3)
33.
All imaginary roots comes in pairs.
a)
True
b)
False
34.
Select polynomial whose zeros and degree are given.
Zeros: – 5(multiplicity of 3), 9(multiplicity of 2), – 2, 4.
a)
(x + 5)3(x - 9)2(x + 2)(x - 4)
b)
(x + 5)3(x - 9)2(x + 2)7(x - 4)7
c)
(x + 5)3(x - 9)2(x + 2)
d)
(x + 5)(x - 9)(x + 2)(x - 4)
35.

Write the polynomial in standard form given the following zeros. x = -2, 1, 4

a)

f(x) = (x+2)(x-1)(x-4)

b)

f(x) =x3 - 3x2 - 6x + 8

c)

f(x) = x3 + 8

d)

f(x) = x3 - 3x2 + 8

36.

How many, and what type, of solutions exist for the function f(x)= x4-10x2-21x-12

a)

4 zeros, 2 real and 2 imaginary

b)

4 zeros, 4 real and 0 imaginary

c)

2 zeros, 2 real and 0 imaginary

d)

2 zeros, 0 real and 2 imaginary

37.

Write an equation of least degree for a polynomial with zeros: -3 ± √7, 4

a)

y = x3 - 2x2 - 64x + 160

b)

y = x3 + 10x2 - 16x - 160

c)

y = x3 + 10x2 + 26x + 8

d)

y = x3 + 2x2 - 22x - 8

38.

Which of the following would be a root with 3i?

a)

3i2

b)

-3i

c)

3i

d)

-3i2

39.

Which of the following would be the correct factored form with roots 2, 5i, and 6?

a)

(x-6)(x-2)(x+5i)(x-5i)

b)

(x+6)(x+2)(x+5i)

c)

(x-6)(x-2)(x-5i)

d)

(x+6)(x+2)(x-5i)

40.

If a+bi is a root of a polynomial, then _______ is also a root.

a)

i2

b)

a-bi

c)

a+bi

d)

-i2

41.
Is this division problem worked correctly?
a)
This is correct!
b)
This is incorrect!
42.
a)
2x2 - x + 1 + 9/(x-2)
b)
2x3 - x2 + x + 9
c)
2x2 - x + 10
d)
x2  - 2x + 1
43.
2x3 - 5x2 + 3x + 7 ÷ x - 2
a)
2x3 - x2 + x + 9
b)
2x2 - x + 1
c)
2x2 - x + 1 + 9/x-2
d)
2x2 - 9x - 15 - 23/x-2
44.
            Is (x-2) a factor of             f(x)= x3-8x2+14x-4?
a)
Yes, (x-2) is a factor. There is a remainder.
b)
No, (x-2) is  not a factor. The remainder is zero.
c)
Yes, (x-2) is a factor. The remainder is zero.
d)
No, (x-2) is  not a factor. There is a remainder. 
45.
Divide the polynomial by the monomial.
a)
15x9 - 8x3
b)
3x6 - 8x3
c)
-5x12
d)
3x6 - 40x3
46.
Divide the polynomial by the monomial.
a)
2x8-8x2-28x
b)
2x8-2x2-7x
c)
8x7-8x-28x
d)
2x7 -2x -7
47.

What are the decreasing intervals?

a)

(- ∞, 0) & (2, ∞ )

b)

(-1, 0) & (2,-4)

c)

(0,2)

d)

(0, -4) & (0, 2)

48.

What are the increasing intervals?

a)

(- ∞, 0) & (2, ∞ )

b)

(-1, 0) & (2,4)

c)

(0,2) & (-3, -7)

d)

(-8, -3) & (-7, 8)

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