Free Printable Chapter 2 Polynomial Function Review

1.

Simplify: (m⁹)²

a)

m¹¹

b)

2m⁹

c)

m¹⁸

d)

m^4.5

2.

Simplify: (-5p)²

a)

-25p²

b)

25p²

c)

-5p²

d)

5p²

3.

Simplify: (5p⁹q³)(2pq⁷)

a)

7p¹⁰q¹⁰

b)

10p⁹q²¹

c)

10p¹⁰q¹⁰

d)

10p⁸q^-4

4.

Simplify: $\frac{6m^7}{\left(4m^3\right)^2}$

a)

$\frac{6m}{16}$

b)

$\frac{3m}{8}$

c)

$\frac{3}{8m}$

d)

$\frac{3m}{4}$

5.

Simplify: $3n^5\cdot5n^{10}$

a)

$15n^5$

b)

$8n^{15}$

c)

$15n^{50}$

d)

$15n^{15}$

6.

Simplify: $\left(2a^3b^4c^3\right)^2\cdot\left(4a^2bc^3\right)$

a)

$16a^8b^9c^9$

b)

$8a^8b^9c^9$

c)

$8a^6b^5c^6$

d)

$16a^5b^5c^6$

7.

Simplify: $\left(3x^5\right)^6$

a)

$18x^{30}$

b)

$729x^{11}$

c)

$3^6x^{30}$

d)

$729x^{30}$

8.

Simplify $\left(\frac{1}{3}\right)^{-3}$

a)

1/9

b)

1/27

c)

27

d)

-27

9.

Simplify

a)

y²

b)

y³⁵

c)

y¹²

d)

y¹⁴

10.

Rewrite using a positive exponent.
w^-13

a)

-w¹³

b)

¹/_w¹³

c)

¹/_w^-13

d)

w¹³

11.

Simplify.

a)

y¹⁵

b)

y⁵

c)

y²

d)

2y⁵

12.

In the above graph complete the following end behavior:
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____

a)

-∞
-∞

b)

+∞
-∞

c)

-∞
+∞

d)

+∞
+∞

13.

In the above graph complete the following end behavior: (f(x)=y)
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____

a)

-∞
-∞

b)

+∞
-∞

c)

-∞
+∞

d)

+∞
+∞

14.

Describe the end behavior of the graph.

a)

x → -∞, f(x) → ∞ and x→∞, f(x) →⁻∞

b)

x → -∞, f(x) → ∞ and x→∞, f(x) →∞

c)

x → -∞, f(x) → ∞ and x→∞, f(x) → 0

d)

x → -∞,f(x) → -∞and x→ ∞, f(x) → ∞

15.

Describe the end behavior of the graph.

a)

x →∞, y→⁻∞ and x →⁻∞,y→⁻∞

b)

x →∞, y→∞ and x→⁻∞, y→∞

c)

x →∞, y→∞ and x→⁻∞, y→0

d)

x →∞,y→∞ and x→⁻∞, y→⁻∞

16.

Which function has this end behavior?

a)

-x²-3x+1

b)

-x³+2x²+3

c)

x⁴+3x³-4x+1

d)

x⁵-4x⁴+2x²-1

17.

Divide: $\frac{x^4+2x^3+2x+4}{x+2}$

a)

$x^3+2x^2$

b)

$x^3+2$

c)

$x^3+4x^2+8x+18+\frac{42}{x+2}$

d)

$x^3+4x^2+10x+24$

18.

Divide: $\frac{5x^3-x^2+6}{x-4}$

a)

$5x^2-21x+84-\frac{330}{x-4}$

b)

$5x^2+19x+82$

c)

$5x^2+19x+76+\frac{310}{x-4}$

d)

$5x^2+19x+\frac{82}{x-4}$

19.

Divide: $\frac{x^3-12x^2+47x-60}{x-3}$

a)

$x^2-9x+20$

b)

$x^3-9x^2+20x$

c)

$x^2-15x+92+\frac{216}{x-3}$

d)

$x^2+9x+20$

20.

Divide: $\frac{27x^3+64}{3x+4}$

a)

$27x^2-36x+48$

b)

$9x^2-12x+16$

c)

$27x^2+28x$

d)

$27x^2+28$

21.

Divide: $\frac{2x^3-9x^2+15}{2x-5}$

a)

$2x^2-4x-10-\frac{10}{2x-5}$

b)

$x^2-2x-5-\frac{10}{2x-5}$

c)

$x^2-2x-5-\frac{5}{2x-5}$

d)

$2x^2-4x+5$

22.

Divide: $\frac{9x^3+12x^2+15x+4}{3x+1}$

a)

$9x^2+9x+12-\frac{8}{3x+1}$

b)

$3x^2+3x+12-\frac{8}{3x+1}$

c)

$9x^2+9x+12$

d)

$3x^2+3x+4$

23.

Which term must be inserted in the dividend before you begin long division?

$\left(2x^3+5x^2+9\right)\div\left(x+3\right)$

a)

$0x^4$

b)

$0x^3$

c)

$0x^2$

d)

$0x$

24.

What is the remainder when a³ - 4 is divided by a+2?

a)

-2

b)

-6

c)

-12

d)

0

25.

Is (x-3) a factor of
(x³- 3x²+ 2x + 2)?

a)

Yes

b)

No

26.

Find all the factors of x³ -3x² -4x +12 given that -2 is a zero.

a)

(x-2) (x+2) (x+3)

b)

(x-2) (x-2) (x+3)

c)

(x+2) (x+2) (x+3)

d)

(x-2) (x+2) (x-3)

27.

Find all the zeros, given that f(-3) = 0
f(x) = 2x³+5x²-6x-9

a)

-1,-3,-3

b)

-1,-3,3/2

c)

3,3,3

d)

-3,2/3,-1

28.

What is the remainder R when the polynomial p(x) is divided by (x-5)?
p(x) = x³- 5x²+ 2x - 10

a)

0

b)

2x-10

c)

-2x-10

d)

2x+10

29.

Is (x-4) a factor of (x³ +x² -16x-16)?

a)

YES

b)

NO

30.

Is (x-3) a factor of
(x³- 3x²+ 2x + 2)?

a)

Yes

b)

No

31.

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.

32.

According to this work, is x-3 a factor of $p\left(x\right)=5x^3-2x^2+x-120$ ?

a)

Yes, x-3 is a factor of p(x) since the remainder is 0.

b)

No, x-3 is not a factor of p(x) since the remainder is 0.

33.

This work shows $x^2-3x+5\div x-2$ . What information does this reveal?

a)

x-2 is not a factor of $x^2-3x+5$ since the remainder is 3.

b)

x-2 is a factor of $x^2-3x+5$ since the remainder is 3.

34.

Simplify the expression.

$\left(7k^2+2k\right)-\left(4k^3+k^2-3k\right)$

a)

$-4k^3+6k^2+5k$

b)

$4k^3+6k^2+5k$

c)

$4k^3+6k^2-k$

d)

$11k^3+8k^2-k$

35.

Name the polynomial by degree and number of terms.

$5x^3+6x^2+1$

a)

linear polynomial

b)

quartic binomial

c)

cubic polynomial

d)

cubic trinomial

36.

Name the polynomial by degree and number of terms

$-4x^4+10x^3+2x^2+2$

a)

linear polynomial

b)

quartic polynomial

c)

quadratic trinomial

d)

quartic binomial

37.

Name the polynomial by degree and number of terms.

$-n^6-2n^4$

a)

sixth degree binomial

b)

fourth degree binomial

c)

sixth degree trinomial

d)

fourth degree binomial

38.

Factor $x^2-4$

a)

$\left(x-2\right)\left(x+2\right)$

b)

$\left(x-4\right)\left(x+4\right)$

c)

$\left(2x-2\right)\left(2x+2\right)$

d)

$\left(x-4\right)\left(x+2\right)$

39.

What method should you use to factor the polynomial?

x² - 36

a)

Factor by Grouping

b)

Factor out the GCF

c)

Difference of Squares

d)

Difference of 2 Cubes

40.

What method should you use to factor the polynomial?

5n³-10n²+3n-6

a)

Factor by Grouping

b)

Factor out the GCF

c)

Difference of Squares

d)

Trinomials (ac,b,T-chart)

41.

What method should you use to factor the polynomial?

n³-216

a)

Sum of 2 Cubes

b)

Factor out the GCF

c)

Difference of Squares

d)

Difference of 2 Cubes

42.

What method should you use to factor the polynomial?

2n³+54

a)

Sum of 2 Cubes

b)

Factor out the GCF

c)

Difference of Squares

d)

Difference of 2 Cubes

43.

Factor Completely. $8x^2-200$

a)

$8\left(x+5\right)\left(x-5\right)$

b)

$8\left(x^2-25\right)$

c)

$4\left(2x^2-50\right)$

d)

$4\left(2x+25\right)\left(2x-25\right)$

44.

Factor Completely. $4x^2+24x-64$

a)

$4\left(x+8\right)\left(x-2\right)$

b)

$4(x^2+6x-16)$

c)

$4\left(x^2+24x-16\right)$

d)

$4\left(x-8\right)\left(x+2\right)$

45.

Factor: x³ + 512

a)

(x + 8)(x² - 8x + 64)

b)

(x + 8)(x² + 8x -64)

c)

(x-8)(x + 2)

d)

(x - 8)(x² - 8x - 64)

46.

Write 4x³+2x²-6x in factored form.

a)

2x(2x-3)(x+1)

b)

4x(2x+3)(x-1)

c)

2x(2x+3)(x-1)

d)

4x(2x-3)(x+1)

47.

Factor this difference of cubes:
x³ - 343

a)

(x + 7) (x² - 7x + 49)

b)

(x² + 1) (x - 343)

c)

(x - 7) (x² + 7x + 49)

d)

(x² - 343) (x + 1)

48.

Factor by grouping:

4p³ + 8p² + 3p + 6

a)

(2p²+3)(p+2)

b)

(2p²+6)(p+4)

c)

(4p²+3)(p+2)

d)

(4p²+8p)(3p+6)

49.

Factor by grouping:
x³+7x²-2x-14

a)

(x²-2)(x-7)

b)

(x²+2)(x-7)

c)

(x²+2)(x+7)

d)

(x²-2)(x+7)

50.

Factor: x⁶-x⁴-25x²+25=0

a)

(3x-1)(x+1)(x²-5)(3x²+5)=0

b)

(x-1)(x+1)(x²-5)(x²+5)=0

c)

x(x-1)(x²-5)(x²+5)=0

d)

(x-1)(x+3)(x²-5)(2x²+5)=0

51.

The polynomial
f(x) = 5x⁴ + 2x³ + 2x − 7 can have, at most, how many solutions?

a)

5

b)

4

c)

3

d)

2

52.

Determine the end behavior of the graph of
f(x) = -3x³ + 2x - x⁴

a)

As x →∞, f(x) →∞.
As x→-∞, f(x) →-∞.

b)

As x →∞, f(x) →∞.
As x→-∞, f(x) →∞.

c)

As x →∞, f(x) →-∞.
As x→-∞, f(x) →∞.

d)

As x →∞, f(x) →-∞.
As x→-∞, f(x) →-∞.

53.

Which of the following functions could represent the graph shown?

a)

f(x) = -2x⁵

b)

f(x) = -2x⁴ + 7x³ + 3x² -5x + 8

c)

f(x) = 2x⁵ + 3x⁴ - 3x³ + 5x² - 3x + 4

d)

None of these functions could represent the graph shown.

54.

What are the zeros of the graph?

a)

-4, -1, 2, 1 multiplicity 2

b)

-4, -1, 1, 2

c)

4, 1, -2, -1 multiplicity 2

d)

4, 1, -1, -2

55.

What are the zeros of the function?

a)

4,1

b)

3,1,-2,-5

c)

-3, -1, 2, 5

d)

-2,4

56.

What does multiplicity mean in terms of the roots of an equations?

a)

To clone a polynomial

b)

How many times a particular number is a zero for a given polynomial.

c)

how many times a polynomial function crosses the x-axis

d)

how many end behaviors a polynomial has

57.

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

58.

What are the zeros of the polynomial function?
y = x(x - 6)(x + 5)

a)

0, 6, -5

b)

6, -5

c)

0, -6, 5

d)

1, -6, 5

59.

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)

60.

Describe the multiplicity of each zero.

a)

-4 multiplicity of 2, -2 multiplicity of 2

b)

-4 multiplicity of 1, -2 multiplicity of 1

c)

2 multiplicity of -4, 2 multiplicity of -2

d)

-4 multiplicity of 1, -2 multiplicity of 2

61.

If the graph of a function crosses the x-axis, what does that mean about the multiplicity of that zero?

a)

Even

b)

Odd

c)

None

62.

Solve the following quadratic equation: $4x^2-9=0$

a)

A. $x=\frac{3}{2}$ & $x=-\frac{3}{2}$

b)

B. $x=\frac{2}{3}$ & $x=\frac{-2}{3}$

c)

C. $x=\frac{9}{4}$

d)

D. $x=\frac{4}{9}$

e)

I'm unsure of how to solve

63.

Solve the following polynomial. $0=x^3-3x^2-4x+12$ (select all that apply)

a)

$x=\pm2$

b)

$x=3$

c)

$x=1$

d)

$x=0$

e)

I'm unsure of how to solve

64.

Find all zeros for the polynomial
P(x) = x³ -3x²-5x+15

a)

3, √5

b)

3, √5, -√5

c)

-3, √5, -√5

d)

-3, 5i, -5i

e)

I'm unsure of how to solve

65.

a)

b)

c)

d)

66.

a)

b)

c)

d)

67.

a)

b)

c)

d)

68.

a)

b)

c)

d)

69.

a)

b)

c)

d)

70.

The blue dot on this graph represents a(n)...

a)

Absolute Maximum

b)

Absolute Minimum

c)

Relative Maximum

d)

Relative Minimum

71.

What is the Absolute Min?

a)

$-6$

b)

$36$

c)

$+\infty$

d)

$-\infty$

72.

What is the Relative Max?

a)

$36$

b)

$-6$

c)

$+\infty$

d)

$-\infty$

73.

What are the Relative Maxima of this graph?

a)

$3.9$ only

b)

$5$ only

c)

$-3.3$ and $-2.5$

d)

$5$ and $3.9$

e)

No Relative Maxima

74.

(T/F) The function shown has an Absolute Minimum.

a)

True

b)

False

c)

Cannot be determined

75.

(T/F) The function shown has an Relative Minimum.

a)

True

b)

False

c)

Cannot be determined

76.

What are the relative maxima of the graph?

a)

$0,\ \infty$

b)

$0$

c)

$\infty$

d)

There is no maxima

77.

What are the relative minima of the graph?

a)

$-4,\ -1$

b)

$-2$

c)

$0$

d)

There is no minima

78.

What is the degree of the function: $f\left(x\right)=-3x^4\left(x+6\right)^3\left(x+1\right)^2\left(x-2\right)^5$ ?

(a)

Chapter 2 Polynomial Function Review

Total questions: 78

Worksheet time: 4hrs 10mins

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