Free Printable Polynomials Review

1.

Add: (3x² + 2x + 1) + (2x² - 4x - 5) + (3x - 1)

a)

5x² + 6x - 7

b)

8x²- 3x - 5

c)

5x²+ x - 5

d)

6x² + 8x + 5

2.

(x+7)(x+4)

a)

$x^2+4x+7$

b)

$x^2+11x+28$

c)

$7x^2+4+11$

3.

Divide: $\frac{6x^2+7x-20}{2x+5}$

a)

$3x^2-4x$

b)

$6x^2-8x$

c)

6x-8

d)

3x-4

4.

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

a)

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

b)

$x^2-9x+20$

c)

$x^2+9x+20$

d)

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

5.

Find the remainder

$\left(2x^3-5x-7\right)\div\left(x+2\right)$

a)

11

b)

-9

c)

-1

d)

-13

6.

What is the remainder when $x^4-5$ is divided by x+3? Verify using the remainder theorem.

a)

7

b)

81

c)

76

7.

Combine like terms to simplify:

(5x + 2) + (4x - 5)

a)

9x -3

b)

-9x-7

c)

9x+7

d)

x+7

8.

(x³-x²+4) - (3x³-2x²+3)

a)

-2x³-3x²+7

b)

-2x³+x²+1

c)

2x³-3x³-1

d)

4x³-3x²+7

9.

Simplify:
2x ( -2x -3)

a)

-4x - 3

b)

x² - 3

c)

-4x² - 6x

d)

-4x - 6

10.

(x - 5)(x + 1)

a)

x² - 4x - 5

b)

x² + 6x - 5

c)

x² - 5x - 4

d)

x² - 4x - 4

11.

(x - 3)(x +10)

a)

x² - 7x + 13

b)

x² - 6x - 30

c)

x² + 7x - 30

d)

x² + 13x + 30

12.

(x + 7)(x - 2)

a)

x² - 5x + 5

b)

x²- 9x - 14

c)

x² - 5x - 14

d)

x² + 5x - 14

13.

(2x - 1)(x + 2)

a)

2x² + 3x - 2

b)

2x² - 5x - 2

c)

2x² + 3x + 2

d)

2x² - 5x + 2

14.

(4x+1)(5x−2)

a)

20x² + 3x − 2

b)

20x² − 11x + 5

c)

20x² − 18x + 2

d)

20x² − 3x − 2

15.

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

a)

$x^3+7x^2+19x+21$

b)

$x^2+19x+7x+7$

c)

$x^3+x^2+19x+7$

16.

2x³(x²−2x − 3)

a)

2x⁶- 4x³ - 6x³

b)

2x⁵−4x⁴ − 6x³

c)

-2x⁵−4x⁴ − 6x³

d)

-2x⁶−4x³ − 6x³

17.

(5x+2)(x²-3x+6)

a)

5x³- 17x²+24x +12

b)

5x³+ 17x² - 24x +12

c)

5x³ - 13x² + 24x +12

d)

5x³ +13x² - 24x - 12

18.

(5x+2)(x²-3x+6)

a)

5x³- 17x²+24x +12

b)

5x³+ 17x² - 24x +12

c)

5x³ - 13x² + 24x +12

d)

5x³ +13x² - 24x - 12

19.

(5x+2)(x²-3x+6)

a)

5x³- 17x²+24x +12

b)

5x³+ 17x² - 24x +12

c)

5x³ - 13x² + 24x +12

d)

5x³ +13x² - 24x - 12

20.

Multiply (5x+2)(x²-3x+6)

a)

5x³- 17x²+24x +12

b)

5x³+ 17x² - 24x +12

c)

5x³ - 13x² + 24x +12

d)

5x³ +13x² - 24x - 12

21.

Find the values of the zeros of the function y=(x+2)(x-3)(3x-5)

a)

x=-2, x=3, x=5/3

b)

x=2, x=-3, x= -5/3

c)

x=-2, x=3, x=3/5

d)

x=2, x=-3, x=-3/5

22.

What are the zeros of the function?

a)

4, 1

b)

-3, -1, 2, 5

c)

-3, -1, 30, 2, 5

d)

3, 1, -2, -5

23.

What are the roots of the function $y=\left(x+2\right)\left(x-7\right)^3$

a)

2, 7 multiplicity 3

b)

-2, -7 mulitplicity 3

c)

-2, 7 mulitplicity 3

d)

2, -7 multiplicity 3

24.

State the zeros of the polynomial function $f\left(x\right)=x\left(x+3\right)^2\left(x-2\right)$

a)

0, 2, -3

b)

0, 2, -3 multiplicity 2

c)

2, -3 mulitiplicity 2

d)

0, -2, 3 multiplicity 2

25.

How many zeros does the polynomial function $f\left(x\right)=3x^4+4x^{2\ }+8$ have?

a)

2

b)

3

c)

4

d)

6

26.

Write the polynomial in standard form given the zeros, x=0, -2, 1

a)

$y=x^{2\ }+x-2$

b)

$y=x^4+x^3-2x^2$

c)

$y=x^{3\ }+x^2-2x$

d)

$y=x^{3\ }-x^2-2x$

27.

Which of the following is the correct equation for the function graphed?

a)

$f\left(x\right)=\left(x-1\right)^{2\ }\left(x+2\right)^{2\ }$

b)

$f\left(x\right)=\left(x+1\right)^2\left(x-2\right)^{2\ }$

c)

$f\left(x\right)=\left(x-1\right)\left(x+2\right)$

d)

$f\left(x\right)=\left(x+1\right)\left(x-2\right)$

28.

What is the equation in factored form of the function graphed?

a)

$f\left(x\right)=-\left(x+4\right)\left(x+1\right)^2\left(x-2\right)\left(x-4\right)$

b)

$f\left(x\right)=-\left(x-4\right)\left(x-1\right)^2\left(x+2\right)\left(x+4\right)$

c)

$f\left(x\right)=\left(x+4\right)\left(x+1\right)^{2\ }\left(x-2\right)\left(x-4\right)$

d)

$f\left(x\right)=\left(x-4\right)\left(x-1\right)^{2\ }\left(x=2\right)\left(x+4\right)$

29.

Which is a possible equation in factored form of the function in the graph?

a)

$y=\left(x+2\right)\left(x-1\right)^2$

b)

$y=\left(x-2\right)\left(x+4\right)\left(x+1\right)^2$

c)

$y=-\left(x+2\right)\left(x-1\right)^2$

d)

$y=-\left(x+1\right)^2\left(x-2\right)$

30.

What is the degree of the polynomial? $y=-4x^5+3x^2-8x+1$

a)

8

b)

4

c)

5

d)

7

31.

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

32.

If the there is a turning point on the x-axis, what does that mean about the multiplicity of that zero?

a)

Even

b)

Odd

c)

None

33.

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

34.

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

35.

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

36.

Odd Multiplicities have which of the following effects on the x-axis?

a)

Cross the x-axis

b)

Turn on the x-axis

37.

Which of the following is a 5th degree trinomial with a leading coefficient of -2?

a)

-2x⁵ + 3x - 1

b)

5x^-2 +3x - 1

c)

-2x⁵ + 3x⁴ + 2x³ + x² - 10

d)

2x + 5

38.

What is the constant in the polynomial x²-2x+5?

a)

1

b)

2

c)

5

d)

0

39.

What is the leading coefficient in the polynomial 3x²-2x+5?

a)

3

b)

2

c)

5

d)

0

40.

What is the leading coefficient?
f(x)=5x²+3x³-2x+1

a)

5

b)

3

c)

-2

d)

1

41.

Classify by the DEGREE:
4x³ - 5x² + 2x - 1

a)

Degree of 1

b)

Degree of 2

c)

Degree of 3

d)

Degree of 4

42.

Classify by the DEGREE:
2x² - 5

a)

Degree of 1

b)

Degree of 2

c)

Degree of 3

d)

Degree of 4

43.

Classify by the DEGREE:
3x - 2

a)

Degree of 1

b)

Degree of 2

c)

Degree of 3

d)

Degree of 4

44.

What was the name of the goddess of war and love in ancient Babylon?

a)

Marduk

b)

Ishtar

c)

Shamash

d)

Hammurabi

45.

What is another way to say "where a function crosses the x-axis"?

a)

x-intercept

b)

zero

c)

root

d)

all of these.

46.

Which best describes the multiplicity of a root?

a)

It is the number of times the corresponding factor is repeated

b)

It is the highest degree of the polynomial

c)

It is the number of times x is multiplied by itself

d)

It is the number of x-intercepts on a graph

47.

Which of the following could be the equation for the polynomial shown?

a)

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

b)

f(x)=(x-1)(2x+1)²(x-3)

c)

f(x)=(x-1)²(2x+1)(x-3)

d)

f(x)=(x-1)(2x+1)(x-3)²

e)

None of these would match the graph

48.

If 𝒙²+𝟑𝒙+𝟕 is divided by 𝒙+𝟐, then what is the remainder?

a)

0

b)

-3

c)

9

d)

5

49.

$\left(2x^3-5x^2-4x-25\right)\div\left(x-4\right)$

a)

$2x^2+3x+8+\frac{-57}{x-4}$

b)

$2x^2-13x-56$

c)

$2x^2+3x+8+\frac{7}{x-4}$

d)

$2x^2-3x-16+-\frac{-89}{x-4}$

50.

Which root has even multiplicity?

a)

1

b)

-4

c)

-1

d)

2

51.

Find all rational zeros, one zero has been given.
f(x) = x³-5x²-2x+24; -2

a)

-2,1,0

b)

-2,-3,-4

c)

4,3,-2

d)

0,0,0

52.

Find all rational zeros, one zero has been given.
f(x) = x³-3x²-x+3; 3

a)

2,4,3

b)

-1,1,3

c)

3,2,1

d)

4,5,6

53.

Factor:
x³-12x²+47x-60=0 when 5 is a root.

a)

(x-3)(x-4)(x-5)=0

b)

(x+1)(x-4)(x-5)=0

c)

(x-3)(x-4)(2x-5)=0

d)

(x-5)(x-4)(x-5)=0

54.

Find all the real zeros of the function
f(x) = 2x³ - 19x² + 38x + 24 given that x-4 is a factor.

a)

x = 1/2, -6

b)

x = -1/2, 6

c)

x = 4, -1/2, 6

d)

x = -4, 1/2, -6

55.

How could you determine if x-2 is a factor of 2x³-5x²+x-2?

a)

Use synthetic division and see if the quotient is even

b)

Ask the person sitting next to me

c)

Use synthetic division and see if the remainder is zero

d)

Flip a coin

56.

The degree of the function is...

a)

the size of it

b)

the number of terms

c)

the greatest exponent on the variable

d)

a BS in mathematics

57.

$\left(2x+7\right)\left(2x^2+5x-4\right)$

a)

$4x^3+24x^2+27x-28$

b)

$3x^3+23x^2+63x+55$

c)

$x^3-1$

d)

$3x^3-13x^2+22x-16$

58.

$\left(x-2\right)\left(3x^2-7x+8\right)$

a)

$4x^3+24x^2+27x-28$

b)

$3x^3+23x^2+63x+55$

c)

$x^3-1$

d)

$3x^3-13x^2+22x-16$

59.

$\left(x^2+x+1\right)\left(x-1\right)$

a)

$4x^3+24x^2+27x-28$

b)

$3x^3+23x^2+63x+55$

c)

$x^3-1$

d)

$3x^3-13x^2+22x-16$

60.

$\left(3x+5\right)\left(x^2+6x+11\right)$

a)

$4x^3+24x^2+27x-28$

b)

$3x^3+23x^2+63x+55$

c)

$x^3-1$

d)

$3x^3-13x^2+22x-16$

61.

For synthetic division, what would be the number in the left hand box?

a)

0

b)

1

c)

2

d)

3

62.

What is the quotient?

a)

x - 7

b)

x²- 7

c)

x + 7

d)

x²+ 3x - 54

63.

(2x³ + 7x² - 6x - 8) ÷ (x + 4)

a)

2x² - x - 2

b)

2x³ - x² - 2x

c)

2x² + 15x + 54 + 208/x+4

d)

2x³ + 15x² + 54x + 208

64.

Divide using synthetic division
(2x³ + 4x² - 5) by (x + 3).

a)

2x² + 2x - 4 R(-12)

b)

2x² - 2x + 6 R(-23)

c)

2x² - 2x + 8 R(-20)

d)

2x² - 4x + 1 R0

65.

Find the quotient:

(2x³ + 5x² + 9) ÷ (x + 3)

a)

2x² - x + 3

b)

2x³ - x² + 3x

c)

2x² + 11x + 33 + 108/x+3

d)

2x² - 5x + 12

66.

(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

67.

-2x²+4x+48 ÷ x+4

a)

-2x+12

b)

2x+12

c)

-4x+9

d)

4x+9

68.

(3x³ + 5x - 1) ÷ (x + 1)

a)

3x³ - 3x² + 8x - 9

b)

3x² - 3x + 8 - 9/x+1

c)

3x² + 3x + 8 + 7/x+1

d)

3x³ + 3x² + 8x + 7

69.

(2x³ + 5x² + 9) ÷ (x + 3)

a)

2x² - x + 3

b)

2x³ - x² + 3x

c)

2x² + 11x + 33 + 108/x+3

d)

2x² - 5x + 12

70.

x²-6x+8 ÷ x-2

a)

x-6

b)

x-9 R=2

c)

x-4

d)

x-8 R=3

71.

(3x³ - 2x² - 7x + 6) ÷ (x + 1)

a)

3x³ - 5x² - 2x + 8

b)

3x² + x - 6

c)

3x² - 5x - 2 + 8/x+1

d)

3x³ + x² - 6x

72.

What is the location of the absolute maximum for the graphed function?

a)

x = 1

b)

x = 3

c)

x = 4

d)

x = 5

e)

Does Not Exist

73.

How many extrema (max and mins) are in the picture?

a)

2

b)

3

c)

4

d)

5

74.

How many extrema are there in this graph?

a)

2 max, 2 min

b)

3 max, 2 min

c)

2 man, 3 min

d)

3 increasing intervals, 2 decreasing intervals

e)

2 increasing intervals, 3 decreasing intervals

75.

Identify the local minimum

a)

x = 8

b)

x = 4

c)

$\infty$

d)

x = 2

76.

What is the location of the relative maximum within the given interval of the graphed function?

-5\le x\le0

a)

x = -4

b)

x = -2

c)

x = 0

d)

x = 3

e)

Does Not Exist

77.

Divide:

(4x² - 24x + 35) / (2x - 5)

a)

2x - 7

b)

2x - 12

c)

2x + 12

d)

2x + 7

78.

Divide:

(4x³ - 2x² - 3) by (2x² - 1).

a)

2x - 1 + (2x - 4)/(2x² - 1)

b)

2x + 3 + (x - 3)/(2x² - 1)

c)

2x - 1

d)

2x + 3 + (3x-5)/(2x² - 1)

79.

Divide:

(x³+ 3x²- 4x - 12) by (x²+ x - 6)

a)

x - 2

b)

x⁵+ 6

c)

x + 2

d)

x²+ 2

Polynomials Review

Total questions: 79

Worksheet time: 7hrs 35mins

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