Free Printable Operations with Polynomials

1.

Simplify to an equivalent expression BUT leave in exponent form.
4³⋅4⁵

a)

4⁸

b)

16⁸

c)

4¹⁵

d)

16¹⁵

2.

Simplify (2m⁴)(5m²)

a)

10m⁶

b)

10m⁸

c)

7m⁶

d)

7m⁸

3.

Simplify the expression.
x⁴ (x¹²)

a)

x³

b)

x⁴⁸

c)

x¹⁶

d)

x⁸

4.

X²⋅ X³⋅ X⁴⋅ X

a)

x⁹

b)

x²⁴

c)

x¹⁰

d)

x²⁵

5.

Simplify the following expression:

(xyz)⁰ =

a)

0

b)

1

c)

xyz

d)

-1

6.

True or False:

a)

True

b)

False

7.

Evaluate using the quotient rule:

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

8.

x⁶y⁹÷ x²y⁵

a)

x⁸y¹⁴

b)

x^-4y^-4

c)

x⁴y⁴

d)

x^-8y^-14

9.

Simplify: $\frac{9h^6}{3h^3}$

a)

$3h^9$

b)

$3h^{3\ }$

c)

$3h^{18}$

d)

$h^{3\ }$

10.

$\left(\frac{x^4}{x^2}\right)^3$ Click on the play button if you need a hint

a)

$x^8$

b)

$x^6$

c)

$x^3$

d)

$x^9$

11.

$\left(\frac{x^5}{x^7}\right)^2$ Click on the play button if you need a hint.

a)

$x^4$

b)

$x^{24}$

c)

$x^{-4}$

d)

$x^5$

12.

Simplify

a)

\frac{x^{28}y^{12}}{x^2y}

b)

$\frac{x^{28}y^{12}}{x^8y^4}$

c)

$x^{20}y^8$

13.

Simplify using your exponent rule(s) (2x³y)⁶

a)

2x¹⁸y⁶

b)

64x¹⁸y⁶

c)

64x³y⁶

d)

2x³y⁶

14.

Using exponents, simplify the following expression:

(2⁸)²

a)

2¹⁶

b)

2¹⁰

c)

2⁶

d)

2⁴

15.

Using exponents, simplify the following expression:

\frac{x^5}{x^3}

a)

x²

b)

x

c)

1

d)

x⁸

16.

Simplify: (m⁹)²

a)

m¹¹

b)

2m⁹

c)

m¹⁸

d)

m^4.5

17.

Simplify: (-5p)²

a)

-25p²

b)

25p²

c)

-5p²

d)

5p²

18.

Simplify: (5p⁹q³)(2pq⁷)

a)

7p¹⁰q¹⁰

b)

10p⁹q²¹

c)

10p¹⁰q¹⁰

d)

10p⁸q^-4

19.

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

a)

$\frac{6m}{16}$

b)

$\frac{3m}{8}$

c)

$\frac{3}{8m}$

d)

$\frac{3m}{4}$

20.

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

a)

$15n^5$

b)

$8n^{15}$

c)

$15n^{50}$

d)

$15n^{15}$

21.

Simplify: $10x^8\cdot9x$

a)

$90x^8$

b)

$19x^9$

c)

$90x^9$

d)

$19x^9$

22.

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)

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

23.

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

a)

$18x^{30}$

b)

$729x^{11}$

c)

$3^6x^{30}$

d)

$729x^{30}$

24.

Simplify: $\left(2m\right)^5$

a)

$10m^5$

b)

$32m^5$

c)

$25m^5$

d)

$\frac{1}{2m^5}$

25.

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

a)

$5x^4$

b)

$-5x^4$

c)

$5x^3$

d)

$-5x^3$

26.

Simplify: $\left(3k^5\right)\left(-2k^3\right)$

a)

$6k^8$

b)

$-6k^{15}$

c)

$6k^{15}$

d)

$-6k^8$

27.

Simplify the following: $\left(4x^3\right)^4$

a)

$16x^7$

b)

$4^4x^7$

c)

$256x^{12}$

d)

$16x^{12}$

28.

(2x³y)⁶

a)

2x¹⁸y⁶

b)

64x¹⁸y⁶

c)

64x³y⁶

d)

2x³y⁶

29.

Simplify (-4r⁵)(2r⁸)

a)

-8r¹³

b)

-2r¹³

c)

-8r⁴⁰

d)

-2y⁴⁰

30.

-3xy³ . (4xy)²

a)

-12x³y⁵

b)

-48x²y⁴

c)

-48x³y⁵

d)

-12x²y⁶

31.

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

a)

1/9

b)

1/27

c)

27

d)

-27

32.

Simplify

a)

y²

b)

y³⁵

c)

y¹²

d)

y¹⁴

33.

According to exponent rules, when we divide the same base, we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

34.

Rewrite using a positive exponent.
w^-13

a)

-w¹³

b)

¹/_w¹³

c)

¹/_w^-13

d)

w¹³

35.

Simplify.

a)

y¹⁵

b)

y⁵

c)

y²

d)

2y⁵

36.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

37.

According to exponent rules, when we divide powers we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

38.

According to exponent rules, when we multiply powers we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

39.

According to exponent rules, when we raise a power to a power we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

40.

Find the sum.
(2x² + 5x - 7) + ( 3 - 4x² + 6x)

a)

2x²+ 3x +1

b)

-2x²- 11x -4

c)

2x² + 5x -7

d)

-2x² + 11x -4

41.

Simplify:

a)

9n³ + 4n

b)

7n³+ 6

c)

-3n³+ 2

d)

7n⁶ + 6

42.

Is b + 8 a monomial?

a)

yes

b)

no

43.

Which of the following are examples of like terms?

a)

2 and 2x

b)

y³and x³

c)

y and x

d)

-3x and 3x

44.

Add the polynomials.
(2x + 5y) + (3x - 2y)

a)

3x + 5y

b)

5x + 3y

c)

5x + 7y

d)

7xy + 1xy

45.

What is the correct name of the following:
3x + 5y² - 3

a)

monomial

b)

binomial

c)

trinomial

d)

polynomial

46.

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

a)

x_² + 6x + 8

b)

2x²+ 5x - 7

c)

-x²-6x + 8

d)

-2x² + 11x - 4

47.

Add the polynomial (-3x + 4) + (8x - 5)

a)

5x - 9

b)

5x - 1

c)

11x - 1

d)

11x - 9

e)

None of these

48.

(2x + 5y - z) + (-6x - 4y + 7z)

a)

-4x +6y + 6z

b)

4x + y + 6z

c)

-4x - y + 6z

d)

-4x + y + 6z

e)

None of these

49.

Classify by number of terms:

3x² – 8x + 1

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

e)

Constant

50.

(3x²+xy-5y²) + (2x²-xy+3y²)

a)

5x²-2xy+8y²

b)

5x²-2y²

c)

5x²+2y²

d)

5x²+2xy-8y²

e)

None of these

51.

(2x + 5y - z) + (-6x - 4y + 7z)

a)

-4x² +6y² + 6z²

b)

4x + y + 6z

c)

-4x² - y² + 6z²

d)

-4x + y + 6z

e)

None of these

52.

What is the correct name of the following:

3xy + 4x + 5y + 6

a)

monomial

b)

binomial

c)

trinomial

d)

polynomial

e)

Constant

53.

(2x-1)(x+5)

a)

$2x^2+9x-5$

b)

$2x+5x-1x$

c)

$2x^2-1x+5$

54.

(3n-4)(3n-4)

a)

$9n^2-24n+16$

b)

$3n^2-4x+8$

c)

$n^2-24n+16$

55.

(8m-2)(8m+2)

a)

$63m^2+2$

b)

$64m^2-4$

c)

$8m^2-2$

56.

(x+5)(x-6)

a)

$x^2-6x-30$

b)

$x^2-x-30$

c)

$x^2+5x-6$

57.

(2x-9)(2x+4)

a)

$4x^2+4x+4$

b)

$2x^2-9x+4$

c)

$4x^2-10x-36$

58.

$\left(m+5\right)\left(m^2+4m-8\right)$

a)

$m^3+4m^2-8m+5m^2+20m-40$

b)

$m^2+40m+m^3$

c)

$m^3+9m^2+12m-40$

59.

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

a)

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

b)

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

c)

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

60.

Simplify:
2x ( -2x -3)

a)

-4x - 3

b)

x² - 3

c)

-4x² - 6x

d)

-4x - 6

61.

Find the product:
(2x+3)²

a)

2x+3+2x+3

b)

4x²+12x+9

c)

4x²+9

d)

16x²+9

62.

2x³(x²−2x − 3)

a)

2x⁶- 4x³ - 6x³

b)

2x⁵−4x⁴ − 6x³

c)

-2x⁵−4x⁴ − 6x³

d)

-2x⁶−4x³ − 6x³

63.

(4p − 1)(4p - 1)

a)

16p² + 1

b)

16p² − 1

c)

16p² − 8p + 1

d)

16p² + 8p + 1

64.

Simplify the expression so there are no negative exponents.
$9^{-2}$

a)

$-9^2$

b)

$9^2$

c)

$\frac{1}{9^2}$

d)

$-\frac{1}{9^2}$

65.

Simplify the following expressions. No negative exponents in the answer.

$2x^4\cdot3x^5$

a)

$6x^{20}$

b)

$5x^9$

c)

$6x^9$

d)

$5x^{20}$

66.

Simplify the following expressions. No negative exponents in the answer.

$8y^{-5}\cdot3y^2$

a)

$24y^{-3}$

b)

$\frac{11}{y^3}$

c)

$\frac{24}{y^7}$

d)

$\frac{24}{y^3}$

67.

Simplify the following expressions. No negative exponents in the answer.

$5m^4n^{-1}\cdot7n^{-2}n^4$

a)

$\frac{35n^3}{m^2}$

b)

$12m^2n^3$

c)

$35m^6n^5$

d)

$35m^2n^3$

68.

Simplify the following expressions. No negative exponents in the answers.

$\left(6p^0\right)^4$

a)

$24p^4$

b)

$1296$

c)

$24$

d)

$1296p^4$

69.

Simplify the following expressions. No negative exponents in the answer.

$a^3b^{-6}\cdot a^5b^{-2}$

a)

$a^8b^{-8}$

b)

$\frac{a^{15}}{b^{12}}$

c)

$\frac{a^8}{b^8}$

d)

$a^{15}b^{-12}$

70.

Perform the given operation with the polynomial. Order and complete them if necessary.

$\left(6-4x^2+5x\right)+\left(7x^2+6x-10\right)$

a)

$3x^2+11x-4$

b)

$11x^2+11x+16$

c)

$3x^2+x-16$

d)

$3x^2-10x+6$

71.

Perform the given operation with the polynomial. Order and complete them if necessary.

$\left(-8x-4+9x^2\right)+\left(-6+3x^2-7x\right)$

a)

$6x^2-x-2$

b)

$6x^2-x-10$

c)

$12x^2-x-10$

d)

$12x^2-15x-10$

72.

Perform the given operation with the polynomial. Order and complete them if necessary.

$\left(4x^3-6x^2+5x-11\right)+\left(2x^3+8x^2+13\right)$

a)

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

b)

$8x^3+48x^2+5x-24$

c)

$6x^3+14x^2+2$

d)

$8x^3+10x^2+5x-10$

73.

Perform the given operation with the polynomial. Order and complete them if necessary.

$\left(-7x^2+3x-4\right)-\left(5x^2-9x+1\right)$

a)

$-2x^2-6x-3$

b)

$-35x^2-27x-4$

c)

$12x^2-12x+5$

d)

$-12x^2+12x-5$

74.

Perform the given operation with the polynomial. Order and complete them if necessary.

$\left(9-8x^3+3x^2+5x\right)-\left(-4x^3-10+6x^2\right)$

a)

$-12x^3+9x^2+5x-1$

b)

$-4x^3-3x^2+5x+19$

c)

$12x^3+9x^2+5x-19$

d)

$4x^3+3x^2-5x+19$

75.

Perform the given operation with the polynomial. Order and complete them if necessary.

$\left(-7x^4+11x-14x^3+1\right)-\left(12x^3+4x^2-8x+2\right)$

a)

$-7x^4-12x^3+4x^2-3x+3$

b)

$-7x^4+26x^3+4x^2-19x+1$

c)

$-7x^4+26x^3+4x^2+88x+2$

d)

$-7x^4-26x^3+4x^2+19x-1$

Operations with Polynomials

Total questions: 75

Worksheet time: 3hrs 42mins

Similar Resources on Wayground