Free Printable Practice test: Polynomials, exponent rules and factorin

1.

Simply:

a)

-1k⁴ +17k² +22

b)

-7k⁸ + 11k⁴-6

c)

-7k⁴- 11k² +6

d)

7k⁴ - 5k²

2.

Simplify:

a)

0

b)

-3n³ +8n

c)

-3n⁶

d)

-6n³

3.

a)

A

b)

B

c)

C

d)

D

4.

Simplify the expression: $(3x^2 + 5x - 7) + (2x^2 - 3x + 4)$ .

a)

$5x^2 + 2x - 3$

b)

$5x^2 + 8x - 3$

c)

$x^2 + 2x - 3$

d)

$5x^2 + 2x + 11$

5.

Subtract the polynomial $(4x^3 - 2x^2 + x - 5)$ from $(6x^3 + x^2 - 3x + 2)$ .

a)

$2x^3 + 3x^2 - 4x + 7$

b)

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

c)

$10x^3 - x^2 - 2x + 7$

d)

$2x^3 + 3x^2 + 4x + 7$

6.

Add the polynomials $(x^2 + 4x + 6)$ and $(3x^2 - 2x + 1)$ .

a)

$4x^2 + 2x + 7$

b)

$4x^2 + 6x + 7$

c)

$4x^2 + 2x + 5$

d)

$4x^2 + 6x + 5$

7.

Simplify the expression: $2(x^2 + 3x - 4) - (x^2 - 2x + 5)$ .

a)

$x^2 + 8x - 13$

b)

$x^2 + 8x - 3$

c)

$x^2 + 4x - 13$

d)

$3x^2 + 8x - 13$

8.

Combine like terms in the expression: $5x^2 - 3x + 4x^2 + 7x - 2$ .

a)

$9x^2 + 4x - 2$

b)

$9x^2 + 4x + 2$

c)

$9x^2 + 10x - 2$

d)

$9x^2 + 10x + 2$

9.

Distribute and simplify: $3(x - 2) + 4(2x + 1)$ .

a)

$11x + 1$

b)

$11x - 2$

c)

$11x + 4$

d)

$11x - 4$

10.

Subtract the polynomial $(2x^2 - 3x + 4)$ from $(5x^2 + x - 6)$ .

a)

$3x^2 + 4x - 10$

b)

$3x^2 + 4x - 2$

c)

$3x^2 + 2x - 10$

d)

$3x^2 + 2x - 2$

11.

Add the polynomials $(2x^3 - x^2 + 3x)$ and $(x^3 + 4x^2 - 2x + 5)$ .

a)

$3x^3 + 3x^2 + x + 5$

b)

$3x^3 + 3x^2 + x$

c)

$3x^3 + 3x^2 + x + 5$

d)

$3x^3 + 3x^2 + x - 5$

12.

Simplify the expression: $(x^2 + 2x - 3) - (2x^2 - 4x + 5)$ .

a)

$-x^2 + 6x - 8$

b)

$-x^2 + 6x + 2$

c)

$-x^2 - 2x - 8$

d)

$-x^2 - 2x + 2$

13.

Combine like terms in the expression: $7x^2 - 4x + 3x^2 + 5x - 6$ .

a)

$10x^2 + x - 6$

b)

$10x^2 + x + 6$

c)

$10x^2 + 9x - 6$

d)

$10x^2 + 9x + 6$

14.

Distribute and simplify: $4(x + 3) - 2(2x - 5)$ .

a)

$4x + 22$

b)

$4x + 16$

c)

$4x + 14$

d)

$4x + 18$

15.

Subtract the polynomial $(3x^2 - 5x + 7)$ from $(6x^2 + 2x - 4)$ .

a)

$3x^2 + 7x - 11$

b)

$3x^2 + 7x + 3$

c)

$3x^2 + 7x - 3$

d)

$3x^2 + 7x + 11$

16.

Match each expression to its simplified form.

1. $\left(m+8\right)^2$ (a)

2. $\left(m-8\right)^2$ (b)

3. $\left(m-8\right)\left(m+8\right)$ (c)

4. $m\left(m+8\right)$ (d)

5. $m\left(m-8\right)$ (e)

Choose from the below words

$m^2+16m+64$

$m^2-16m+64$

$m^2-64$

$m^2+8m$

$m^2-8m$

$a^2-6a-9$

$m^2+16m-64$

$m^2+64$

$m^2+8$

$m^2-8$

17.

Simplify: $\left(2x^2-x+3\right)\left(4x-1\right)$ .

18.

According to exponent rules, when we multiply two power with the same base we _______ the exponents.
Example: c⁶ ⋅ c⁴

a)

add

b)

subtract

c)

multiply

d)

divide

19.

According to exponent rules, when we divide two powers with the same base we _______ the exponents.
Example: h⁸/h³

a)

add

b)

subtract

c)

multiply

d)

divide

20.

According to exponent rules, when we raise the power to a power we _______ the exponents.
Example: (d²)⁵

a)

add

b)

subtract

c)

multiply

d)

divide

21.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

22.

$15a^5b^2+4a^5b^2$

a)

$19a^{10}b^4$

b)

$19a^5b^2$

c)

$60a^{10}b^4$

d)

$60a^5b^2$

23.

$-7m-m^2+4m^2-3m$

a)

$-7m^6$

b)

$-7m^2$

c)

$3m^2-10m$

d)

$-10m^2-3m$

24.

Simplify the following monomial: $-5a^2b^{2\ }-\ a^2b^2$

a)

$-6a^2b^2$

b)

$-4a^2b^2$

c)

$6a^2b^2$

d)

$6a^2b^2$

25.

(3c²)(10c⁷)

a)

13c⁹

b)

30c⁵

c)

30c⁹

d)

-30c⁹

26.

2n⁴ * 5n⁴

a)

7n⁴

b)

10n¹⁶

c)

10n⁸

d)

none of the above

27.

6m³n³* 8m²n³

a)

48m⁵n⁹

b)

48m⁶n⁶

c)

48m⁵n⁶

d)

none of the above

28.

(2x³y)⁶

a)

2x¹⁸y⁶

b)

64x¹⁸y⁶

c)

64x³y⁶

d)

2x³y⁶

29.

Simplify:

(7y⁴)²

a)

7y⁶

b)

14y⁸

c)

49y⁶

d)

49y⁸

30.

Simplify.

(3x⁴y⁵)²

a)

9x⁸y¹⁰

b)

6x⁸y¹⁰

c)

3x⁸y¹⁰

d)

x⁸y¹⁰

31.

subtract the exponents and simplify the fraction

a)

8x⁴

b)

8x⁸

c)

6x⁴

d)

6x⁸

32.

Simplify.(subtract the exponents and simplify the fraction)

a)

12x⁶y⁴

b)

12x¹⁰y⁶

c)

22x¹⁰y⁶

d)

22x⁶y⁶

33.

Simplify. (subtract the exponents and simplify the fraction)

a)

2y²⁴

b)

2¹⁰

c)

2y¹⁰

d)

2y¹⁴

34.

Simplify the expression so that it contains only positive exponents.

a)

b)

c)

d)

35.

Simplify each expression so that it contains only positive exponents.

a)

b)

c)

d)

36.

Simplify each expression so that it contains only positive exponents.

a)

b)

c)

d)

37.

a)

$6c^{16}d^7-13c^{16}d^7$

b)

$-7c^{16}d^7$

c)

$6c^3d^{\frac{10}{3}}-13c^{16}d^7$

d)

$-3c^{16}d^7$

38.

$\left(\frac{-3x^{-6}y^{-1}z^{-2}}{6x^{-2}yz^{-5}}\right)^{-2}\ -\ \left(3x^3y^2z^{-2}\right)^3\cdot\left(x^{-1}y^{-2}\right)$

a)

$\frac{23x^5y^3}{z^3}$

b)

$x^8y^4z^6$

c)

$\frac{-23x^8y^4}{z^6}$

d)

$\frac{x^8y^4}{z^6}$

39.

Give the correct name for

3x

a)

Cubic Monomial

b)

Linear Binomial

c)

Linear Monomial

d)

Cubic Binomial

40.

Give the correct name for
3x²+4x-7

a)

Quadratic trinomial

b)

linear binomial

c)

Quartic trinomail

d)

Linear Trinomail

41.

Give the correct name for
2x³+5x

a)

Linear Binomial

b)

Cubic Binomial

c)

Quadratic Trinomial

d)

Linear Trinomial

42.

Which polynomial is written in standard form?

a)

-3x + 8x² + 9x³ - 11

b)

9x³ + 8x²- 3x - 11

c)

8x²+ 9x³ -11 - 3x

d)

-11 - 3x + 8x² + 9x³

43.

What is the name of the polynomial?
7x + 1

a)

Monomial

b)

Binomial

c)

Trinomial

d)

Polynomial

44.

Given the polynomial:
9x⁷ + 3x⁶ - 5 + x²What is the constant?

a)

9

b)

3

c)

5

d)

-5

45.

What is the degree of the polynomial:
x² + 2x³ - x

a)

2

b)

3

c)

1

d)

6

46.

What is the name for this polynomial? 2x² + 3x - 1

a)

Quadratic Trinomial

b)

Linear Binomial

c)

Quartic Trinomial

d)

Quintic Trinomial

47.

What is the name for this polynomial? 3z

a)

Constant Monomial

b)

Linear Binomial

c)

Linear Monomial

d)

Bionic Monomial

48.

What is the name of this polynomial? 4x³ - 2x² + 7x - 3

a)

Septic Polynomial with Four Terms

b)

Quadratic Polynomial with Four Terms

c)

Quintic Polynomial with Four Terms

d)

Cubic Polynomial with Four Terms

49.

What is the name of this polynomial? 6a⁴ + 7a³ + 8

a)

Linear Trinomial

b)

4th Degree Binomial

c)

2nd Degree Trinomial

d)

Quartic Trinomial

50.

What is the name of this polynomial? 3

a)

Constant Monomial

b)

Linear Monomial

c)

Quartic Monomial

d)

Cubic Monomial

51.

If a polynomial is considered linear, its degree is...

a)

2

b)

3

c)

1

d)

98

52.

If a polynomial is a constant, its degree is...

a)

1

b)

0

c)

-1

d)

98

53.

Classify this polynomial by its degree and number of terms: 4x³

a)

Cubic monomial

b)

Linear binomial

c)

Cubic binomial

d)

6th degree (sextic) monomial

54.

When I am a dividing by a monomial, I should _______ the coefficients and ________ the exponents for each term.

a)

add, subtract

b)

subtract , divide

c)

divide, divide

d)

divide, subtract

55.

$\frac{20x^2}{5x}$

a)

$15x$

b)

$4x$

c)

$15x^2$

d)

$25x$

56.

$\frac{\left(5x^2-15y^3\right)}{5}$

a)

$x^2-3y^3$

b)

$x^2-15y^3$

c)

$10x^2-20y^3$

d)

$5x^2-3y^3$

57.

$\frac{\left(8x^4+6x^3-10x^2\right)}{2x^2}$

a)

$4x^2+3x-5$

b)

$4x^2+3x^{1.5}-5x$

c)

$6x^2+4x-12$

d)

$6x^2+4x^{1.5}-12x$

58.

$\frac{\left(-18x^5-12x^3-6x^2\right)}{-3x}$

a)

$-15x^4-9x^2-3x$

b)

$-6x^4-4x^2-2x$

c)

$6x^4+4x^2+2x$

d)

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

59.

$\frac{81x^9-54x^6+27x^3}{9x}$

a)

$9x^9-6x^6+3x^3$

b)

$9x^8-6x^5+3x^2$

c)

$9x^{10}-6x^7+3x^4$

d)

$81x^8-6x^5+3x^2$

60.

$\frac{\left(x^6y^8-x^4y^6+x^2y^4\right)}{x^2y^2}$

a)

$x^4y^6-x^2y^4+y^2$

b)

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

c)

$x^8y^{10}-x^6y^8+x^4y^6$

d)

$0x^4y^6-0x^2y^4+0y^2$

61.

Dividing Powers:

a)

-5x⁴y³

b)

5x⁴y³

c)

5x¹⁰y⁷

d)

-5x¹⁰y⁷

62.

Dividing Powers:

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

d)

none of the above

63.

Evaluate

a)

24x⁴

b)

8x³

c)

8x⁴

d)

24x⁸

64.

Divide the following:

a)

7m³ -2m²n⁶ + 3mn⁸

b)

7m¹¹ - 2m¹⁰n⁸ + 3m⁹n¹⁰

c)

7m³ - 6m⁶n⁷ + 9m⁵n⁹

d)

36

65.

Divide the polynomial by the monomial.

a)

2x⁸-8x²-28x

b)

2x⁸-2x²-7x

c)

8x⁷-8x-28x

d)

2x⁷-2x -7

66.

What is the GCF of 18 and 24?

a)

3

b)

6

c)

8

d)

9

67.

What is the GCF between the following monomials?

15k³ and 18k

a)

3k²

b)

3k³

c)

3k

d)

5k

68.

What is the GCF between the following monomials?

56x² and 30x

a)

4x

b)

6x

c)

2x

d)

x

69.

What is the GCF between the following monomials?

32x³ 48x²

a)

8x²

b)

16x²

c)

16x

d)

96x³

70.

What is the GCF between the following monomials?

10a⁴ , 16a , 10a²

a)

2a

b)

2a²

c)

10a

d)

10a²

71.

What is the GCF between the following monomials?

a²b⁵ and a³b³

a)

a²b³

b)

a²b⁵

c)

a³b³

d)

a³b⁵

72.

What is the GCF between the following monomials?

10a²b³ and 20a²b²?

a)

20a²b³

b)

10a²b³

c)

20ab²

d)

10a²b²

73.

What is the GCF between the following monomials?

5xy³z, 26x²y⁵z², 10x³yz²

a)

5xyz

b)

x²y³z⁵

c)

2xy³z

d)

xyz

74.

What is the GCF between the following monomials?

12t³, 30t², 48t

a)

12t

b)

6t³

c)

6t

d)

12t³

75.

Find the greatest common factor of

6x⁴y³, 12x⁴y² , 6x³y²

a)

6

b)

6xy

c)

6x³y²

d)

6x⁹y⁶

76.

What is the GCF between the following monomials?

24x⁹ , 36x⁶ , 60x³?

a)

6x

b)

6x³

c)

24x⁹

d)

24x

77.

Factor the polynomial by finding the GCF:

2x + 4

a)

2 (x + 2)

b)

2 (x + 4)

c)

4 (x + 4)

d)

4 (x + 2)

78.

Factor the polynomial by finding the GCF:

5x² + 20x

a)

5 (x + 4)

b)

5x (x + 4)

c)

5 (x² + 4)

d)

5x² (x + 4)

79.

Factor the polynomial by finding the GCF:

24x² + 30x

a)

6 (4x² + 5)

b)

6x (4x + 5)

c)

2 (12x² + 15)

d)

2x (12x + 15)

80.

Factor the polynomial by finding the GCF:

x⁵ + x⁴ + x²

a)

x³ (x² + x + 1)

b)

x (x⁴ + x³ + x)

c)

x² (x³ + x²)

d)

x² (x³ + x² + 1)

81.

Factor the polynomial by finding the GCF:

6x²y - 18xy²

a)

6 (x - 3y)

b)

6xy (x - 3y)

c)

6xy² (x - 3)

d)

6x²y (3y - 1)

82.

Factor the polynomial by finding the GCF:

3x²y² + 14x²y + 15x

a)

y (3x²y + 14x² + 15x)

b)

xy (3xy + 14x + 15)

c)

x² (3y² + 14y + 15)

d)

x (3xy² + 14xy + 15)

83.

Factor the polynomial by finding the GCF:

15x⁴ + 20x³ - 25x

a)

5x² (3x² + 4x - 5)

b)

5x (3x³ + 4x² - 5x)

c)

5x (3x³ + 4x² - 5)

d)

5 (3x⁴ + 4x³ - 5x)

84.

Factor the polynomial by finding the GCF:

4x²yz²- 14xy²z

a)

xyz (4xz - 14y)

b)

2xyz (2xz - 7y)

c)

2xyz (2xy - 7z)

d)

xyz (4xy - 14z)

85.

Factor the polynomial by finding the GCF:

10x²y⁵ + 25x⁴y²

a)

5x²y² (5y³ + 2x²)

b)

5x²y² (2y³ + 5x²)

c)

5x²y² (5x² + 5y³)

d)

5x²y² (2x² + 2y³)

86.

Factor the polynomial by finding the GCF:

10x³ + 30x² + 20xy

a)

5x (2x² + 6x + 4y)

b)

10x (x² + 3x + 2y)

c)

10x (x² + 3x + 2)

d)

5x (2x² + 6x + 4)

87.

Factor the polynomial by finding the GCF:

15x²y⁴ + 21x³y⁷

a)

xy (15xy³ + 21x²y⁶)

b)

3xy (5xy³ + 6x²y⁶)

c)

x²y⁴ (15 + 21xy³)

d)

3x²y⁴ (5 + 7xy³)

88.

Factor the polynomial by finding the GCF:

12x² + 16x + x

a)

x (12x + 17)

b)

4x (3x + 4)

c)

4 (3x + 4)

d)

x² (12x + 17)

89.

Factor the polynomial by finding the GCF:

13y³ - 25y + y

a)

y (13y² + 24)

b)

13y (y² + 2)

c)

y (13y² - 24)

d)

13y (y² - 2)

90.

Factor the polynomial by finding the GCF:

15x³ + 20x² - 22x + 3x

a)

x (15x² + 20x - 25)

b)

5 (3x² + 4x - 5)

c)

x (15x² + 20x - 19)

d)

5x (3x² + 4x - 5)

91.

Factor the polynomial by finding the GCF:

23x⁹ + 42x⁶ - 11x⁵ + 5x²

a)

x² (23x⁷ - 42x⁴ - 11x³ + 5)

b)

x² (23x⁷ + 42x⁴ - 11x³ + 5x)

c)

x (23x⁸ + 42x⁵ - 11x⁴ + 5x)

d)

x² (23x⁷ + 42x⁴ - 11x³ + 5)

92.

Factor the polynomial by finding the GCF:

23x⁹ + 42x⁶ - 11x⁵ + 5x²

a)

x² (23x⁷ - 42x⁴ - 11x³ + 5)

b)

x² (23x⁷ + 42x⁴ - 11x³ + 5x)

c)

x (23x⁸ + 42x⁵ - 11x⁴ + 5x)

d)

x² (23x⁷ + 42x⁴ - 11x³ + 5)

93.

Factor the polynomial by finding the GCF:

63x⁶y⁸ + 28x¹⁰y⁴ - 42x¹²y¹⁰

a)

7x⁶y⁴ (9y⁴ + 4x⁴ - 6x⁶y⁶)

b)

7x⁶y⁸ (9 + 4x⁴ - 6x⁶y²)

c)

7x⁶y⁴ (9y⁴ + 4x⁵ - 6x⁶y⁶)

d)

7x²y² (9x⁴y⁶ + 4x⁸y² - 6x¹⁰y⁸)

94.

Question: 30x² - 20x + 15.

The answer is 5(6x² - 4x + 3).

True or false. If false, why?

a)

True.

b)

False, because 5 is not a GCF.

c)

False, because 5x is a GCF.

d)

False, because 15 is a GCF.

95.

Question: 20x² - 16x + 2x.

The answer is 2x (10x - 9). True or false.

If false, change the correct answer.

a)

True.

b)

False, the correct answer is 2x (10x - 7)

c)

False, the correct answer is 2 (10x + 7)

d)

False, the correct answer is 2x (10x + 7)

96.

Find the area of a rectangle with length (x - 5) and width (3x + 1).

a)

3x²+16x-5

b)

3x²-14x+5

c)

3x²-14x-5

97.

Choose the correct answer below.

a)

$A=3x^2+9x-5$

b)

$A=5x^2-x+7$

c)

$A=3x^2-x+7$

d)

$A=5x^2+9x-5$

98.

Find the volume of the rectangular prism with length ( x + 2) width ( x - 4) and height ( 2x + 1).

a)

x² -8x

b)

x² -2x -8

c)

2x³-3x² -18x-8

d)

2x³-8

99.

The length of a square is x + 2 units. Find the area.

a)

4x + 8 units squared

b)

x² + 4x + 4 units squared

c)

x² + 4 units squared

d)

Not enough information

100.

What is the perimeter of the backyard?

a)

$2x^2+2x-2$

b)

$x^2+x+2$

c)

$3x^2+5x-12$

d)

$x^2-x$

101.

Multiply the following polynomial by the monomial:

3x(4x² - x - 3)

a)

12x²- 3x- 9

b)

7x³- 3x²- 6x

c)

12x³- 3x²- 9x

d)

12x³- 3x²- 6

102.

What is the Perimeter?

a)

3x - 3 inches

b)

6x - 6 inches

c)

3x - 6 inches

d)

6x - 3 inches

103.

What is the perimeter for the given rectangle:

a)

6x³ - 9x² + 10x - 15

b)

6x² + 1x - 15

c)

6x² + 4x + 4

d)

6x³ + 1x² - 15x

104.

What is the area for the given rectangle:

a)

6x³ - 9x² + 10x - 15

b)

6x² + 1x - 15

c)

6x² + 4x + 4

d)

6x³ + 1x² - 15x

105.

A pool has a length of x - 5 and a width of x + 3. What is the area of the pool?

a)

x² - 2x - 15

b)

x² - 8x + 15

c)

x² + 2x - 15

d)

x² + 8x + 15

106.

Zoe is building a rectangular garden. The length of the garden is $3x + 2$ meters and the width is $x - 1$ meters. Find the area of the garden.

a)

$3x^2 - x - 2$

b)

$3x^2 + x - 2$

c)

$3x^2 + 2x - 1$

d)

$3x^2 - 2x + 1$

107.

Michael is designing a square garden with a side length of $2x + 3$ meters. Find the area of the garden.

a)

$4x^2 + 12x + 9$

b)

$4x^2 + 6x + 9$

c)

$4x^2 + 9$

d)

$4x^2 + 12x$

108.

^{The perimeter of the triangle is 10x+20. Find the length of the missing side.}

a)

6x+10

b)

15x+30

c)

5x+10

d)

5x-10

109.

Find a simplified expression for the area of the shaded region. *HINT: Think big minus small

a)

2x²+ 2x + 13

b)

10x + 5

c)

10x + 13

d)

2x²+ 13

110.

The length of a rectangle is 5 in. longer than its width. Which of the following polynomials represent the area of the rectangle? *Hint: Draw and label a picture

a)

5x²

b)

6x

c)

x²+5

d)

x²+5x

111.

Think - what is the length and width of the entire space?

a)

4x + 39

b)

4x² + 78x

c)

4x² + 78x + 308

d)

x²+39x + 308

112.

Choose the correct answer below.

a)

$A=3x^2+9x-5$

b)

$A=5x^2-x+7$

c)

$A=3x^2-x+7$

d)

$A=5x^2+9x-5$

113.

Find the area. $\left(Area\ =\ LW\right)$

a)

A

b)

B

c)

C

d)

D

114.

Find the area of the shaded region.

a)

A

b)

B

c)

C

d)

D

115.

^{The perimeter of the triangle is 10x+20. Find the length of the missing side.}

a)

6x+10

b)

15x+30

c)

5x+10

d)

5x-10

116.

Find a simplified expression for the area of the shaded region. *HINT: Think big minus small

a)

2x²+ 2x + 13

b)

10x + 5

c)

10x + 13

d)

2x²+ 13

117.

The length of a rectangle is 5 in. longer than its width. Which of the following polynomials represent the area of the rectangle? *Hint: Draw and label a picture

a)

5x²

b)

6x

c)

x²+5

d)

x²+5x

118.

Think - what is the length and width of the entire space?

a)

4x + 39

b)

4x² + 78x

c)

4x² + 78x + 308

d)

x²+39x + 308

119.

Choose the correct answer below.

a)

$A=3x^2+9x-5$

b)

$A=5x^2-x+7$

c)

$A=3x^2-x+7$

d)

$A=5x^2+9x-5$

120.

Find the area. $\left(Area\ =\ LW\right)$

a)

A

b)

B

c)

C

d)

D

121.

Find the area of the shaded region.

a)

A

b)

B

c)

C

d)

D

122.

Review Factoring:

b²+ 8b + 7

a)

(b + 4)(b + 3)

b)

(b + 6)(b + 1)

c)

(b + 7)(b +1)

d)

prime

123.

Review Factoring:

x² - 15x + 50

a)

(x - 10)(x - 15)

b)

(x - 10)(x - 5)

c)

(x - 25)²

d)

(x - 5)²

124.

Review Factoring:

x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

125.

Review Factoring:

a² - a - 12

Fill in the blank with your answer make sure you use parentheses

(a)

126.

Review Factoring:

3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

127.

Review Factoring:

2n² + 13n + 15

a)

(5n - 9)(n - 3)

b)

(3n + 7)(n + 4)

c)

(2n + 3)(n + 5)

d)

Not factorable

128.

Review Factoring:

5x² - 13x + 6

a)

(x - 3)(5x - 2)

b)

(5x - 3)(x - 2)

c)

5(x - 3)(x + 2)

d)

Not factorable

129.

Review Factoring:

4h² - 17h + 4

a)

(2h - 2)²

b)

4(h + 4)(h + 1)

c)

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

d)

(h - 4)(4h - 1)

130.

Factor this perfect square trinomial

x² + 24x + 144

a)

(x + 12)²

b)

(x+12)(x-12)

c)

(x - 12)²

d)

(x + 72)²

131.

Factor this perfect square trinomial

x² - 4x + 4

a)

(x + 2)²

b)

(x - 2)²

c)

(x + 4)²

d)

(x - 4)²

132.

Factor this perfect square trinomial:

n²+ 10n + 25

a)

(n + 5)(n - 5)

b)

(n + 25)(n + 1)

c)

(n - 5)²

d)

(n + 5)²

133.

Factor this perfect square trinomial:

4x²+36x+81

a)

(4x+81)²

b)

(2x+9)²

c)

Prime /

Not factorable.

d)

(2x-9)²

134.

Factor this perfect square trinomial:
$49x^2-28x+4$

a)

$\left(7x+2\right)\left(7x-2\right)$

b)

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

c)

$\left(7x-2\right)^2$

d)

$\left(3.5x-1\right)^2$

135.

Which of the following trinomials is a perfect square trinomial?

a)

r² - 6r + 36

b)

4y² + 10y + 25

c)

x² + 16x + 16

d)

9a² - 12a + 4

136.

Factor using a Difference of Squares:
$x^2-121$

a)

$\left(x-11\right)^2$

b)

$\left(x+11\right)\left(x-11\right)$

c)

$\left(x-60.5\right)\left(x+60.5\right)$

d)

$\left(x+11\right)^2$

137.

Factor using a Difference of Squares:

x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

138.

Factor using a Difference of Squares:
$16x^{2\ }-\ 81$

a)

$\left(4x-9\right)^2$

b)

$\left(2x-9\right)^2$

c)

$\left(4x\ +\ 9\right)^2$

d)

$\left(4x+9\right)\left(4x-9\right)$

139.

Factor using a Difference of Squares:

25x²- 100y²

a)

( 5x - 10y) (5x + 10y)

b)

( 5x - 10y)²

c)

Prime

d)

( 5x - 50y) (5x + 50y)

140.

Factor using a Difference of Squares:

Must factor out a GCF first

3x²- 75

a)

3( x + 5 ) ( x - 5 )

b)

Prime

c)

( x + 5 ) ( x - 5 )

d)

3( x - 5 ) ( x - 5 )

141.

Factor using a Difference of Squares:

x²+ 81

a)

Prime (not factorable)

b)

( x - 9 ) ( x + 9 )

c)

( x + 9 ) ( x + 9 )

d)

( x - 9 ) ( x - 9 )

142.

x² + 5x + 6

a)

(x - 3) (x - 2)

b)

(x + 3) (x - 2)

c)

(x + 3) (x + 2)

d)

(x + 2) (x - 3)

143.

x² - 9x + 18

a)

(x + 6) (x + 3)

b)

(x - 6) (x - 3)

c)

(x - 2) (x - 9)

d)

(x + 2) (x + 9)

144.

x² + 8x - 20

a)

(x + 10) (x - 2)

b)

(x + 10) (x + 2)

c)

(x + 5) (x + 4)

d)

(x + 5) (x - 4)

145.

x² - 9x - 22

a)

(x + 11) (x - 2)

b)

(x + 2) (x - 11)

c)

(x - 11) (x - 2)

d)

(x + 2) (x + 11)

146.

x² - 10x + 21

a)

(x + 3) (x - 7)

b)

(x + 7) (x + 3)

c)

(x - 7) (x - 3)

d)

(x + 7) (x - 3)

147.

x² - 6x - 40

a)

(x + 4) (x - 10)

b)

(x + 5) (x - 8)

c)

(x + 10) (x - 4)

d)

(x + 8) (x - 5)

148.

x² + 15x - 100

a)

(x + 4) (x - 25)

b)

(x + 25) (x - 4)

c)

(x + 5) (x - 20)

d)

(x + 20) (x - 5)

149.

x² - 13x - 114

a)

(x + 19) (x - 6)

b)

(x + 6) (x - 19)

c)

(x - 6) (x - 19)

d)

(x + 6) (x + 19)

150.

x² + 19x - 330

a)

(x + 30) (x - 11)

b)

(x + 30) (x + 11)

c)

(x - 11) (x - 30)

d)

(x + 11) (x - 30)

151.

x² + 37x + 132

a)

(x + 4) (x - 33)

b)

(x - 33) (x - 4)

c)

(x + 33) (x - 4)

d)

(x + 33) (x + 4)

152.

One of these trinomials can't factor further, the rest can factor. Which is it?

a)

x² + 10x - 171

b)

x² - 27x + 180

c)

x² + 41x + 330

d)

x² - 24x + 217

153.

Factor
x² - 9x + 18

a)

A. (x - 6)(x - 3)

b)

B. (x + 6)(x - 3)

c)

C. (x - 9)(x - 2)

d)

D. (x - 6)(x + 3)

154.

Factor
n² + 16n + 63

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

155.

Factor by GCF:
17xy - x

a)

17(xy - x)

b)

y(17x - x)

c)

x(17y - 1)

d)

not factorable

156.

Factor completely
k²+7x+10

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

157.

x² + 8x - 20

a)

(x + 10) (x - 2)

b)

(x + 10) (x + 2)

c)

(x + 5) (x + 4)

d)

(x + 5) (x - 4)

158.

x² - 9x + 18

a)

(x + 6) (x + 3)

b)

(x - 6) (x - 3)

c)

(x - 2) (x - 9)

d)

(x + 2) (x + 9)

159.

x² - 9x - 22

a)

(x + 11) (x - 2)

b)

(x + 2) (x - 11)

c)

(x - 11) (x - 2)

d)

(x + 2) (x + 11)

160.

x² + 6x - 27

a)

(x + 3) (x - 9)

b)

(x + 9) (x + 3)

c)

(x - 9) (x - 3)

d)

(x + 9) (x - 3)

161.

x² - 10x + 21

a)

(x + 3) (x - 7)

b)

(x + 7) (x + 3)

c)

(x - 7) (x - 3)

d)

(x + 7) (x - 3)

162.

x² - 6x - 40

a)

(x + 4) (x - 10)

b)

(x + 5) (x - 8)

c)

(x + 10) (x - 4)

d)

(x + 8) (x - 5)

163.

x² + 8x - 9

a)

(x + 9) (x - 1)

b)

(x - 9) (x - 1)

c)

(x + 9) (x + 1)

d)

(x + 1) (x - 9)

164.

x² + 15x - 100

a)

(x + 4) (x - 25)

b)

(x + 25) (x - 4)

c)

(x + 5) (x - 20)

d)

(x + 20) (x - 5)

165.

x² - 13x - 114

a)

(x + 19) (x - 6)

b)

(x + 6) (x - 19)

c)

(x - 6) (x - 19)

d)

(x + 6) (x + 19)

166.

What is the leading coefficient of the polynomial?
7x⁵ - 9x² + 6x

a)

7

b)

5

c)

9

d)

2

167.

What is the leading coefficient of the polynomial?
9x⁵ + 2x⁴ - x³ + 9x² - 2

a)

5

b)

9

c)

2

d)

4

168.

Factor out the GCF

3x³ + 9x

a)

3x (x²+ 3)

b)

3x ( x³ + 9)

c)

x (3x² + 9)

d)

3x (x³ + 3x)

169.

Find the factors

$24m^4n^2\ -\ 16m^3n^3$

a)

$4m^3n^2\left(6m\ -\ 4n\right)$

b)

$8mn\ \left(3m^4n^2\ -\ 2m^3n^3\right)$

c)

$8m^3n^2\ \left(3m\ -\ 2n\right)$

d)

$8m^3n^2\ \left(3mn\ -\ 2mn\right)$

170.

Find ALL the factors

$12x^{10}y^5\ +\ 8x^7y^2$

a)

$\left(3x^3y^3\ +\ 2\right)$

b)

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

c)

$4x^7y^2\ \left(8x^3y^3\ +\ 4\right)$

d)

$4x^7y^2\ \left(\ 3x^{17}y^7\ +\ 2xy\right)$

171.

Factor completely.

$36ab\ +\ 20bc$

a)

$4b\ \left(9a\ +\ 5c\right)$

b)

$2b\left(18a\ +\ 10c\right)$

c)

$4abc\ \left(9a\ +\ 5c\right)$

d)

$4\ \left(9ab\ +\ 5bc\right)$

172.

$9m^2n\ +\ 3mn\ +\ 6mn^5$

a)

$3mn\ \left(3m\ +\ mn\ +\ 2n^4\right)$

b)

$3mn\left(3m\ +\ 2n^4\right)$

c)

$3mn\ \left(3n\ +\ 1\ +\ 2m^4\right)$

d)

$3mn\ \left(3m\ +\ 1\ +\ 2n^4\right)$

173.

Factor Completely

$12a^3b^2\ -\ 18a^4b^3\ +\ 36a^2b^4$

a)

$6a^2b^2\ \left(2b\ -\ 3ab^2\ 6a^2\right)$

b)

$6a^2b^2\ \left(2a\ -\ 3a^2b\ +\ 6b^2\right)$

c)

$3a^2b^2\ \left(4a\ -\ 9a^2b\ +\ 12b^2\right)$

d)

$\left(2a\ -\ 3a^2b\ +\ 6b^2\right)$

Practice test: Polynomials, exponent rules and factorin

Total questions: 173

Worksheet time: 17hrs 0mins

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