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polynomials

Total questions: 105

Worksheet time: 12hrs 44mins

Name

Class

Date

Give the correct name for
2x³+5x

Linear Binomial

Cubic Binomial

Quadratic Trinomial

Linear Trinomial

Find f(0) if f(x) = 5x³ + 2x² +3x

-2

List all possible rational zeros
f(x) = 3x⁵-5x²+x+6

1, 2, 3, 6, -1, -2, -3, -6

1/3,2/3,1,2,3,6,-1/3,-2/3,-1,-2,-3,-6

1/3,2/3,1,2,3,6

Find ALL the zeros of the function
f(x) = x² +2x + 10

-1 + 3i, -1-3i

1 + square root 19, 1- square root 19

2 + 6i , 2 - 6i

-2+6i, -2-6i

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

-2x⁵ + 3x - 1

5x^-2 +3x - 1

-2x⁵ + 3x⁴ + 2x³ + x² - 10

2x + 5

This polynomial has a degree of 2.

Cubic

Quadratic

Linear

Binomial

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

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

What should be the order of the polynomial coefficients if
(3x - 4x³ + 6x⁴ + 1) / (x + 3)

3 0 -4 6 1

6 -4 3 1 0

6 -4 0 3 1

-6 4 0 -3 -1

10.

Is (x-7) a factor of (x²-5x+14)?

Yes

11.

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

YES

12.

Use the remainder theorem to determine the remainder of (10x⁴- 50x³- 800) ÷(x - 6).

-740

1,360

22,960

no remainder

13.

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

Yes

14.

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

-2

-6

-12

15.

Which binomial is a factor of
f(x)= x³ + x² -24x +36?

x + 2

x + 3

x + 6

x + 9

16.

Which binomial is a factor of
f(x)= x³ -6x² +3x +10?

x + 1

x + 2

x + 5

x + 10

17.

-3x²+x+4=0
How many roots does this equation have?

18.

The degree of the polynomial determines the number of roots.

True

False

19.

The largest exponent determines the degree of the polynomial.

True

False

20.

What is the degree of the following polynomial that has 4 real roots and 2 complex roots?

21.

How many roots does the above Polynomial have?

22.

What is the least degree of the graph of the above polynomial?

Not enough information

23.

Based on the end behavior of the polynomial, what best describes the leading coefficient?

a negative real number

a positive real number

an even real number

an odd real number

24.

Based on the end behavior of the polynomial, what is the degree of the polynomial?

a negative real number

a positive real number

an odd real number

an even real number

25.

What is the least degree of the polynomial?

any odd integer

any even integer

26.

Which point does not represent a zero of a polynomial?

(-2, 0)

(-1, 0)

(0, 4)

(2, 0)

27.

Based on the end behavior, the function is most like which of the following?

constant functions

quadratic functions

cubic functions

linear function

28.

What are the linear terms of the polynomial function?

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

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

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

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

29.

Based on the end behavior which option best describes the leading term?

negative coefficient, even degree

negative coefficient, odd degree

negative degree, odd coefficient

negative degree, even coefficient

30.

What are the zeros of the polynomial?

X=5, x=-3(multiplicity of 2)

x=-3, x=5(multiplicity of 2)

x=3, x=-5

x=5

31.

Classify the polynomial by degree.

quartic

quintic

6th degree polynomial

7th degree polynomial

32.

What is the remainder?
(6x² + 19x + 13) ÷ (2x + 5)

-5/2

33.

Write the equation of the polynomial function
zeros: 0, -2, 4
degree: 5
0 has a multiplicity of 3

f(x) = x³(x-2)(x+4)

f(x) = x³(x+2)(x-4)

f(x) = x²(x-2)(x+4)

f(x) = x²(x+2)(x-4)

34.

Is (x-7) a factor of (x²-5x+14)?

Yes

35.

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

2x-10

-2x-10

2x+10

36.

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

Yes

37.

List all possible rational zeros
f(x) = 3x⁵-5x²+x+6

1, 2, 3, 6, -1, -2, -3, -6

1/3,2/3,1,2,3,6,-1/3,-2/3,-1,-2,-3,-6

1/3,2/3,1,2,3,6

38.

Let f(x) = 4x^2 -33x -27. Is k = 9 a zero of the function?

yes

39.

What is the end behavior as x → -∞ f(x)→ ?

-∞

∞

40.

What is the degree classification of this polynomial?
x²+4x-8

binomial

trinomial

quadratic

cubic

41.

Which is an example of a cubic binomial?

x³+5

x²+3

x²+5x-6

5x³

42.

4x - 2

4x + 2

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

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

43.

What id the Degree of the Polynomial?
5x³ - 6x + 1

Linear

Quadratic

Cubic

Quartic

44.

Even Degree
- Leading Coeff.

Even Degree
+ Leading Coeff.

Odd Degree
- Leading Coeff.

Odd Degree
+ Leading Coeff.

45.

Even Degree
- Leading Coeff.

Even Degree
+ Leading Coeff.

Odd Degree
- Leading Coeff.

Odd Degree
+ Leading Coeff.

46.

This function is most likely:

quadratic

cubic

quartic

linear

47.

The polynomial has...

Odd degree, positive leading coefficient.

Odd degree, negative leading coefficient.

Even degree, positive leading coefficient.

Even degree, negative leading coefficient.

48.

What is the end behavior as x → +∞, f(x)→ ?

-∞

∞

49.

f(x) = (x-4)²(x+1)

Even Degree
- Leading Coeff.

Even Degree
+ Leading Coeff.

Odd Degree
- Leading Coeff.

Odd Degree
+ Leading Coeff.

50.

What is the degree of the function graphed here?

51.

The right side of the graph goes ______.
f(x) = -6x⁴ - 2x² + 8

down

52.

Which graph could represent the function f(x) = -x³ - x² + 5x

53.

Identify the degree of the polynomial and the sign of the leading coefficient

Leading Coefficient Positive
Degree - Even

Leading Coefficient Positive
Degree - Odd

Leading Coefficient Negative
Degree - Even

Leading Coefficient Negative
Degree - Odd

54.

Which function has this end behavior?

-1x⁴-3x³+3

-2x⁷+2x⁴+4

3x⁸+3x⁵-4x+7

4x⁵-4x⁴+2x³-9

55.

Describe the behavior of the graph on the interval ( -1, 1)

zero

increasing

median

decreasing

56.

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

-2,1,0

-2,-3,-4

4,3,-2

0,0,0

57.

Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = 2x³ + 5x² - 9x + 5

±1, 5, 1/2, 5/2

±1, 2, 5, 1/2, 5/2

±1, 5

±1, 2, 5, 1/2, 5/2, 2/5

58.

Find all rational zeros, one zero has been given.
f(x) = 2x³+5x²-6x-9; -3

-1,-3,-3

-1,-3,3/2

3,3,3

-3,2/3,-1

59.

List all the possible rational zeros
h(x) = x³- 5x²+2x+12

1,2,3,4,6,12

1,2,6,12

1,2,3,4,6,12,-1,-2,-3,-4,-6,-12

60.

List all of the possible rational zeros
p(x) = 3x²+x+7

-1/3, -7/3, -1, -7, 1/3,7/3,1,7

1/3,7/3,1,7

1, 7, 14, 21

61.

2x³ - 5x² + 3x + 7 ÷ x - 2

2x³ - x² + x + 9

2x² - x + 1

2x² - x + 1 + 9/x-2

2x² - 9x - 15 - 23/x-2

62.

(2x³ + 5x² + 9) ÷ (x + 3)

2x² - x + 3

2x³ - x² + 3x

2x² + 11x + 33 + 108/x+3

2x² - 5x + 12

63.

(3x³ + 5x - 1) ÷ (x + 1)

3x³ - 3x² + 8x - 9

3x² - 3x + 8 - 9/x+1

3x² + 3x + 8 + 7/x+1

3x³ + 3x² + 8x + 7

64.

(2x³ - 5x - 7) ÷ (x - 2)

2x³ - 4x² + 3x - 13

2x³ + 4x² +3x - 1

2x² - 4x + 3 - 13/x-2

2x² + 4x + 3 - 1/x-2

65.

Let f(x) = 4x^2 -33x -27. Is k = 9 a zero of the function?

yes

66.

Let f(x) = 3x^2 - 9x +2.
Is k = -3 a zero of the function?

yes

67.

(3x³ + 5x - 1) ÷ (x + 1)

3x³ - 3x² + 8x - 9

3x² - 3x + 8 - 9/x+1

3x² + 3x + 8 + 7/x+1

3x³ + 3x² + 8x + 7

68.

Use synthetic division:
(2x³ - 5x - 7) ÷ (x - 2)

2x³ - 4x² + 3x - 13

2x³ + 4x² +3x - 1

2x² - 4x + 3 - 13/x-2

2x² + 4x + 3 - 1/x-2

69.

(3x³ + 5x - 1) ÷ (x + 1)

3x³ - 3x² + 8x - 9

3x² - 3x + 8 - 9/(x+1)

3x² + 3x + 8 + 7/(x+1)

3x³ + 3x² + 8x + 7

70.

What are the asymptotes?

x=1, x= 2, y =1, y= 2

x= 2, x=-2, y = 1

x=2 y =-1

x=1 y =2, y =-2

71.

What is the horizontal asymptote?

x = 2

x = 7

y = 2

y = 7

72.

What is the horizontal asymptote of the function given?

y = 2

x = 1

x = 2

y = -1

73.

Where is the removable discontinuity?

x=2

x=2 and x=3

x=-3

x=3

74.

What is/are the vertical asymptote(s)?

x=-2

x=2 and x=3

x=-3

x=3

75.

What is the Vertical Asymptotes?

x= -5

x= 5

x= 6

x= -6

76.

What is the Vertical Asymptotes?

x= -4

x= -4,5

x= -5,5

x= 4

77.

Which asymptotes are determined by looking at the denominator of a function?

vertical

horizontal

slant

none

78.

None

x = -4

x = 3

x = 4

79.

State the vertical asymptote: f(x)=(x-2)/(x+5).

x = -2/5

x = -5/2

x = -5

x = 2

80.

Select the graph that show the corresponding vertical & horizontal asymptotes to this function

81.

What's the horizontal asymptote of the function?

y = 0

No horizontal asymptote

y = 2

y = 4

82.

What's the horizontal asymptote of the function?

y = 0

No horizontal asymptote

y = 1

y = 9

83.

What's the horizontal asymptote of the function?

y = 0

No horizontal asymptote

y = 1/2

y = 1

84.

What's the vertical asymptote of the function?

x = -4, x = 1

x = 4, x = -1

x = -4, x = -1

x = 4, x = 1

85.

What is the domain?

(-∞, ∞)

(-∞, -3) υ (-3, ∞)

(-∞, 1) υ (1, ∞)

86.

What is the domain?

(-∞, ∞)

(-∞, 0) U (0, ∞)

(-∞, -3) U (3, ∞)

(-∞, -3) U (-3, 3) U (3, ∞)

87.

What is the domain?

(-∞, ∞)

(-∞, 1) U (1,∞)

(-∞, 2) U(2, ∞)

88.

Find the domain of the rational function f(x) = x / (x²-25)

(- infinity, -5) U (5, infinity)

(-infinity, -5) U (-5, 5) U (5, infinity)

(- infinity, 5) U (5, infinity)

(- infinity, 25) U (25, infinity)

89.

What is the domain of the following function:

f(x)=3/(x+2)

(-∞,-2)U(2,∞)

(-∞,-2)U(-2,∞)

(-∞,2)U(2,∞)

(-∞,∞)

90.

What value(s) make the expression undefined?

x = - 3 and x = 4

x = 3 and x = - 4

x = 3 only

x = - 4 only

91.

Write an equation for a rational function with an x-intercept of (–1, 0), a hole at x = 3, and a VA at x = 4.

y= (x-1)(x+3) / (x+4)(x+3)

y= (x-4)(x-3) / (x+1)(x-3)

y= (x+1)(x-3) / (x-4)(x-3)

y= (x+4)(x+3) / (x+1)(x+3)

92.

Write an equation of a rational function that has a V.A. at x = 5, and an x- intercept of (3, 0).

y= (x-3) / (x-5)

y= (x+3) / (x+5)

y= (x+3) / (x-5)

y= (x-3) / (x+5)

93.

What are the asymptotes?

x = -3 y = 1

x = 3 y = 1

x = -3 y = -1

x = 3 y = -1

94.

Which is the range of the following?

(−∞, -2) and (-2, +∞)

(−∞, 7) and (7, +∞)

(−∞, -7) and (-7, +∞)

(−∞, 2) and (2, +∞)

95.

Solve the inequality.
2x³+3x²-17x-30<0

(-2.5,-2)U(3,∞)

(-∞,-2.5]U[-2,3]

(-∞,-2.5)U(-2,3)

[-2.5,-2]U[3,∞)

96.

Solve the inequality.
(x-2)(x+3)²(x²+4)≥0

[2,∞)

{-3},[2,∞)

(2,∞)

{ }

97.

Decide if (x-3) is a factor of 3x³+10x²-x-12

Yes, it is a factor

No, it is not a factor

98.

Give the equation of the 4th degree polynomial with zeros: 1 with multiplicity 2 and i.

x² - 4x + 4

x³ - 4x² + 4x +ix² -4ix + 4i

x⁴ - 4x³ + 5x²-4x + 4

x⁴ - 4x³ + 5x²-4x + 4i

99.

(x-3)(x+4)>0

(-∞, -4)U(-4, ∞)

(-4, 3)

(-∞, -4]U[3,∞)

(-∞, -4) U (3, ∞)

100.

(x - 1)(x - 2)(x - 4) ≤0

(-∞, 1)U(2, 4)

(-∞, 1]U[2, 4]

[1, 2]U[4, ∞)

(-1, 4)

101.

(x - 4)(x-2)²(x - 3)²< 0

(-∞, 2)U(2, 3)U(3, 4)

(-∞, 2]U[2, 3]U[3, 4]

(-∞, 4)

(4, ∞)

102.

x² - 2x - 15 ≤ 0

(-∞, -3) U (5, ∞)

(-3, 5)

[-3, 5]

(-∞, -3]U[5, ∞)

103.

2x² - x - 3 ≥ 0

(-∞, ∞)

(-∞, 3/2]

(-∞, -1]U[3/2, ∞)

[-1, 3/2]

104.

x⁴ - 3x² - 10 > 0

(-∞, -√5) U (√5, ∞)

(-∞, -√5] U [√5, ∞)

( -√5,√5)

(-∞, -2) U (√5, ∞)

105.

x³ + 2x² - 4x - 8 > 0 (root x = 2)

(-2, 2) U (2, ∞)

No Solution

[2, ∞)

(2, ∞)

100 %

polynomials

Total questions: 105

Worksheet time: 12hrs 44mins

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