Free Printable IM3 Unit 1 Test Review

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IM3 Unit 1 Test Review

Total questions: 100

Worksheet time: 11hrs 59mins

Name

Class

Date

Factor by using GCF:
8n³ + 2n²

2n²(4n-1)

2n²(4n + 1)

n²(8n+2)

3n(4n+1)

Factor:
80x⁵-70x²-60x⁷

2x²(80x³-70-60x⁶)

10x²(80x⁴-70x-60x⁶)

10x²(8x³-7-6x⁵)

3x²(80x³-40-60x⁵)

Factor:
24c⁵ - 12c³

6(4c⁵ - 2c³)

12c³(2c²)

12c³(2c² - 1)

12c³(2c² - 0)

Factor completely

45xy + 15x³y + 10y

5y (9xy + 3x²+ 2y)

5xy (9 + 3x²+ 2)

5x (9y + 3xy + 2)

5y (9x + 3x³ + 2)

Factor Completely

12abc + 18 ab²c - 6b

6b (2abc + 3b - 1)

6b ( 2ac + 3abc - 1)

6b (2ac + 3abc)

6abc (2 + b)

What is the first question you ask yourself when factoring a polynomial?

How many terms does it have?

Is there a GCF?

What strategy should I use?

Why do I have to learn this?!?!?!

9x²- 49y²

( 3x + 7y) (3x + 7y)

( 3x - 7y) (3x + 7y)

( 3x - 7y) (3x - 7y)

Prime

Factor 4y² – 9.

(2y + 3)(2y – 3)

prime

(2y + 3)(2y + 3)

(2y – 3)(2y – 3)

Factor completely.

121x² - 49

( 11x - 7 ) ²

( 11x - 7 ) ( 11x - 7 )

( 11x + 7 ) ( 11x - 7 )

( 12x + 7 ) ( 12x - 7 )

10.

Factor completely.

49x² + 16

( 7x + 4 ) ( 7x - 4 )

( 7x + 4 ) ( 7x + 4 )

( 7x - 4 ) ²

does not factor (SUM of squares)

11.

Factor: 8x³ - 1

(2x - 1)(4x² + 2x + 1)

(2x + 1)(4x² - 2x + 1)

(2x - 1)(4x² - 2x - 1)

(2x + 1)(4x² +2x + 1)

12.

Factor: 27x³ + 8

(3x + 2)(9x² - 6x + 4)

(9x + 2)(3x² + 18x + 4)

(3x²+4)(9x + 2)

(27x + 8)(x² - 216x + 64)

13.

Complete the formula
a³-b³=

(a-b)(a²+ab+b²)

(a+b)(a²-ab+b²)

(a-b)(a²-ab+b²)

(a+b)(a²+ab+b²)

14.

Factor using differencesum/ of cubes. (use your notes!)
a³ + b³

(a-b)(a²+ab+b²)

(a+b)(a²-ab+b²)

(a-b)(a²-ab+b²)

(a+b)(a²+ab+b²)

15.

x³ - 1000

(x + 10)(x² - 10x + 100)

(x - 10)(x² + 10x + 100)

(x - 1)(x² + 1x + 1)

(x - 5)(x² + 5x + 25)

16.

x²- 400

( x - 200) ( x + 200)

( x + 20) ( x + 20)

Prime

( x - 20) ( x + 20)

17.

64x³ + 1

(4x - 3)(16x² + 12x + 9)

(3x - 1)(9x² + 3x + 1)

(2x - 1)(4x² + 2x + 1)

(4x + 1)(16x² - 4x + 1)

18.

Factor:
x² - 4x + 24

prime

(x + 6)(x - 4)

(x - 8)(x - 3)

(x - 12)(x - 2)

19.

Factor Completely: 3n² - 15n + 18

(n - 2)(n - 3)

3(n + 2)(n + 3)

(3n - 9)(n - 2)

3(n - 3)(n - 2)

20.

Factor Completely: 15t² - 27t - 6

3(5t +1)(t - 2)

(3t - 6)(5t + 1)

3(5t - 1)(t + 2)

(15t + 6)(1t - 6)

21.

Factor Completely: 6x² + 5x - 6

6(x + 1)(x - 6)

(6x + 6)(x - 1)

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

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

22.

Factor: n²- 2n + 1

(n + 1)(n - 1)

(n + 1)²

prime

(n - 1)²

23.

Factor Completely: 5v²- 30v + 40

(5v - 8)(v + 5)

(5v + 5)(v - 8)

5(v - 4)(v - 2)

5(v + 8)(v - 5)

24.

Factor:
2m² + 3m - 9

2(m + 3)(m - 3)

(2m - 3)²

(m + 3)(2m - 3)

(2m + 3)(m - 3)

25.

Factor:
4h² - 17h + 4

(2h - 2)²

4(h + 4)(h + 1)

(2h - 2)(2h + 2)

(h - 4)(4h - 1)

26.

Factor Completely: 16b² + 60b - 100

(4b + 20)(4b - 5)

(16b - 20)(b + 5)

(4b + 10)(4b - 10)

4(b + 5)(4b - 5)

27.

Factor the polynomial completely.

28.

Factor the polynomial completely.

29.

Factor the polynomial completely.

30.

What is the factored form of 5n³-10n²+3n-6

(5n²+3)(n-2)

(5n²-3)(n-2)

(5n³+3)(n-2)

10n(n²-6)

31.

What is the factored form of x³+7x²-2x-14

(x²-2)(x-7)

(x²+2)(x-7)

(x²+2)(x+7)

(x²-2)(x+7)

32.

What is the factored form of 4p³+8p²+3p+6

(2p²+3)(p+2)

(2p²+6)(p+4)

(4p²+3)(p+2)

(4p²+8p)(3p+6)

33.

Factor p³- 3p² - 16p + 48

p² ( p - 3) (p - 3)

(p² - 16) (p - 3)

(p + 4) (p - 4) (p - 3)

34.

Factor x³ + 2x² - 49x - 98

(x² - 49) (x + 2)

(x² - 49) (x + 2) (x + 2)

(x + 7) (x - 7) (x + 2)

35.

30x³+15x²-18x-9

(5x²-3)(6x+1)

(5x²-3)(6x+3)

3(5x²+3)(2x-1)

3(5x²-3)(2x+1)

36.

Classify the following polynomial

quartic quadratic trinomial

quartic polynomial

quadratic trinomial

quartic trinomial

37.

Classify the following polynomial

Quintic Polynomial

Quartic Polynomial

polynomial

38.

Classify the following polynomial

quadratic trinomial

quartic polynomial

quartic trinomial

39.

Classify the following polynomial

quartic polynomial

quadratic polynomial

quartic trinomial

quadratic trinomial

40.

Classify the following polynomial

quartic quadratic trinomial

quartic polynomial

quadratic trinomial

quartic trinomial

41.

Put in Standard Form.
12 - 3x³ - 10x - x²

- 3x³ - x² - 10x + 12

3x³ - x² + 10x + 12

12 - 3x³ - 10x - x²It is in Standard Form.

12 - 10x - 3x³ - x²

42.

Which polynomial is written in standard form?

-3x + 8x² + 9x³ - 11

9x³ + 8x²- 3x - 11

8x²+ 9x³ -11 - 3x

-11 - 3x + 8x² + 9x³

43.

(3x² + 6x - 1) + (4x² + 5x + 9)

-x² + x - 10

x² - x + 10

7x² + 11x + 8

7x² + 11x + 10

44.

-x³(9x⁴ - 2x³ + 7)

-9x¹² + 2x⁹ - 7x³

9x⁷ - 2x⁶ + 7x³

-9x⁷ - 2x³ + 7

-9x⁷ + 2x⁶ - 7x³

45.

Find the sum.
(3y² + y³ - 5) + (4y² -4y + 2y³ + 8)

3y³+ 7y²- 4y + 3

4y² + 3y³ - y + 3

-y⁴ + 2y³-y - 4

4y³+ 3y²-3y + 1

46.

Find the difference.
(3- 2x + 2x²) - (4x -5 +3x²)

x_² + 6x + 8

2x²+ 5x - 7

-x²-6x + 8

-2x² + 11x - 4

47.

Simplify the expression:
(3x⁴ - 4 - 5x²) - (1 - x² + 2x³)

3x⁴ - 2x³ - 4x² - 5

3x⁴ - 7x³ - 4x² - 5

3x⁴ - 7x³ - 4x² - 4

3x⁴ - 5x³ - 4x² - 4

48.

Simplify the expression:
(p³ - 6p⁴ + 1) - (8p⁴ - 8p³ + 7)

-14p⁴ + 9p³ - 6

-14p⁴ + 9p³ + 6

-14p⁴ + 9p³ - 1

-15p⁴ + 9p³ + 6

49.

Find the sum.
(3y² + y³ - 5) + (4y² -4y + 2y³ + 8)

3y³+ 7y²- 4y + 3

4y² + 3y³ - y + 3

-y⁴ + 2y³-y - 4

4y³+ 3y²-3y + 1

50.

Simplify the expression:
(p³ - 6p⁴ + 1) - (8p⁴ - 8p³ + 7)

-14p⁴ + 9p³ - 6

-14p⁴ + 9p³ + 6

-14p⁴ + 9p³ - 1

-15p⁴ + 9p³ + 6

51.

(5x+1)(x+4)

5x² + 19x − 4

5x² + 21x + 4

5x² + 4

5x² − 19x − 4

52.

(4x+1)(5x−2)

20x² + 3x − 2

20x² − 11x + 5

20x² − 18x + 2

20x² − 3x − 2

53.

Simplify the expression.
-3x²( 7x²- x + 4)

-21x⁴ + 3x³ -12x²

7x² - x + 4 (-3x²)

21x⁴+ 3x³+ 12x²

-12x²+ 3x³-21x⁴

54.

-5x⁶(3x² - 12x + 30)

-15x⁸+ 60x⁷- 150x⁶

15x⁸- 60x⁷- 150x⁶

8x⁶- 17x + 35

-8x⁶+ 17x - 35x²

55.

(5x+2)(x²-3x+6)

5x³- 17x²+24x +12

5x³+ 17x² - 24x +12

5x³ - 13x² + 24x +12

5x³ +13x² - 24x - 12

56.

(x-3)(x²+2x+7)

x³-x²+x-21

x³+5x+13x-21

x³-3x²+7x-21

x²+2x-3

57.

What is the perimeter of the rectangle?

x²+8x-5

2x²+16x-10

2x²+10x-8

6x-2

58.

What is the area of the rectangle?

x²+8x-5

3x³+14x²+17x+4

3x³+14x²-17x+4

6x-2

59.

Is this division problem worked correctly?

This is correct!

This is incorrect!

60.

This is correct

This is incorrect

61.

Divide

2x³ + 3x + (7/x-4)

2x² + 3x + 8 + (7/x-4)

2x² + 3x + 8

2x² - x + 10 + (6/x-4)

62.

63.

64.

if f(x) = x³+8x+24, then find f(-2) using synthetic division.

-6

65.

x³-3x²-10x+24 ÷ x+3

x²-7x+5

x-8

x²-6x+8

x+9

66.

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

67.

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

68.

Is (x-2) a factor of f(x)= x³-8x²+14x-4?

Yes, (x-2) is a factor. There is a remainder.

No, (x-2) is not a factor. The remainder is zero.

Yes, (x-2) is a factor. The remainder is zero.

No, (x-2) is not a factor. There is a remainder.

69.

What does it mean to be a factor of a number?

Divides evenly with a remainder of zero.

Divides unevenly with a remainder of 1.

70.

If you are missing an exponent in your polynomial you must put a zero as a coefficient place holder for that exponent

True

False

71.

What is the proper way to write the answer for the following problem?

2x³-x²-25x+12

2x⁴-x³-25x²-12x+0

2x³-x²-25x-12

2x⁴-x³-25x²-12x-0

72.

Cam divided (x⁴ + 3x² - 4x - 2) by factor of (x-2) using synthetic division. His work is shown above. Which best describes his mistake?

Cam wrote the remainder incorrectly.

Cam did not use a zero place holder for the x³ term.

Cam added instead of subtracting the rows.

Cam should have used -2 as his division since the factor was x-2.

73.

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

74.

Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = x³ + 2x² - 6x + 8

±1, ±8

±1, ±2, ±4, ±8

±1, ±2, ±4

1, 2, 4, 8

75.

Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = 3x³ + 2x² - 6x + 7

±1, ±7, ±1/3, ±7/3

±1, 7

±1, ±3, ±7, ±7/3

±1, ±3, ±7, ±1/3, ±7/3

76.

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

77.

Solve by using Rational Root Theorem:
2x³ - 11x² + 12x + 9 = 0

-1, 1, 3

-1, 3/2, 3

-1/2, 3, 3

-1/2, 1, 3

78.

Is (x-2) a factor of f(x)= x³-8x²+14x-4?

Yes, (x-2) is a factor. There is a remainder.

No, (x-2) is not a factor. The remainder is zero.

Yes, (x-2) is a factor. The remainder is zero.

No, (x-2) is not a factor. There is a remainder.

79.

Solve by using Rational Root Theorem:
x³ + 3x² - 6x - 8 = 0

-4, -1, 2

-4, -1, ±√2

1, 2, 4

4,-1,√2

80.

How many zeros does the following function have?
f(x)= x⁵- 3x³ + x

81.

Use the Fundamental Theorem of Algebra to state the number of zeros/solutions/roots of the polynomial.

82.

How many solutions does the polynomial f(x)=3x⁴ + 5x² - 6x have?

83.

What is the proper way to write the answer for the following problem?

2x³-x²-25x-12

2x⁴-x³-25x²-12x+0

84.

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

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

f(x) =x³ - 3x² - 6x + 8

f(x) = x³+ 8

f(x) = x³ - 3x² + 8

85.

Write the polynomial with the given zeros

86.

f(x)=(x+4)(x-3)(x-2)

List the zeros for this function.

x = -4, x = 3, x = -2

x = -4, x = 3, x = 2

x = -4, x = -3, x = 2

x = 4, x = 3, x = 2

87.

x²+ 12x + 32 = 0

x = -4, 8

x = 4, 8

x = -4, -8

x = 0, 12

88.

Solve x² + x – 72 = 0.

x = -8

x = -8 or x = 9

x = 8 or x = -9

x = 9

89.

What is the first step in solving
(x + 2)(x - 3) = 0 ?

Plug in zero for x

Solve for x

FOIL

Set each binomial factor equal to zero

90.

How many zeros does the polynomial function
P(x) = 3x⁴+4x-8 have?

91.

If p(x) = 9x⁴- 45x³+ 37x² + x +2, use synthetic substitution to find p(2).

p(2) = 656

p(2) = 652

p(2) = -64

p(2) = -368

92.

How many zeros do you expect the polynomial function
P(x) = 3x³+4x-8 to have?

93.

Solve 10x³- 40x² + 40x = 0.

x= 0 and x = 2

x = 0

x = 2

x = -2, x = 0, and x = 2

94.

Find the zeros of the function f(x) = 4x⁴ - 8x² + 4.

x = -1 and x = 1

x = 1

x = -1

no solution

95.

Find all real solutions of x³ - 5x² - 2x + 24 = 0.

x = -2, x = 3, and x = 4

x = -2 and x = 4

x = 3 and x = 4

x = -2

96.

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

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

f(x) =x³ - 3x² - 6x + 8

f(x) = x³+ 8

f(x) = x³ - 3x² + 8

97.

Write a polynomial function of least degree with integral coefficients that has the given zeros.

98.

Find the zeros of the polynomial function: f(x)= (x-3)(x+2)²(x-5)

x= 3,2,5

x= 3, -2, 5

x= -3, 2, -5

x= -2, -3, -5

99.

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

(x - 1)(x + 1)

x(x - 1)(x + 1)

x²(x - 1)(x + 1)

x(x - 1)(x - 1)

100.

How many total roots/zeros are there in the polynomial.

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IM3 Unit 1 Test Review

Total questions: 100

Worksheet time: 11hrs 59mins

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