Free Printable Adding, Subtracting and Multiplying Polynomials Practice

1.

Add the polynomials.
(3x³ + 3x² – 4x + 5) + (x³ – 2x² + x – 4)

a)

4x³ + 1x² – 3x + 1

b)

2x³ + 1x² - 5x + 9

c)

6x³ + 1x - 1x² - 3

d)

3x⁵ +1x - 1x⁵ - 3x

2.

(3x + 4y - 3z) - (2x - 6y + 7z)

a)

x + 10y - 10z

b)

-x +10y - 10z

c)

x -10y - 10z

d)

-x -10y - 10z

3.

Simplify the expression.
(4a³ - 8a - 4a²) + (7a³ - 7 - 6a)

a)

11a³ - 4a² - 14a - 7

b)

5a³ - 4a² - 14a - 7

c)

5a³ - 4a² - 20a - 7

d)

5a³ - 9a² - 20a - 7

4.

(5x⁴- 4x³- 2x² + x - 19) - (x⁴+ 5x³ + 8x² + x + 5)

a)

4x⁴- 9x³- 10x²- 24

b)

4x⁴- 9x³ - 10x²- 2x - 24

c)

4x⁴ - 9x³ - 10x² + 2x - 24

d)

-4x⁴ - 9x³ - 10x² - 24

5.

How many terms are in the following polynomial?
3x³ - 2y + 8x -16

a)

1

b)

2

c)

4

d)

-16

6.

What is the degree of this polynomial?
4xy² + 3x - 5

a)

2

b)

3

c)

4

d)

5

7.

What is the degree of this term?
-7xyz²

a)

3

b)

4

c)

-7

d)

7

8.

What is the constant in the polynomial?
-2xyz + 3x² - 2y² - 6z² + 32

a)

-2

b)

3

c)

-6

d)

32

9.

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

a)

monomial

b)

binomial

c)

trinomial

d)

polynomial

10.

What is the correct name of the following:
3xy + 4x + 5y + 6

a)

monomial

b)

binomial

c)

trinomial

d)

polynomial

11.

What is the degree of this polynomial?
52a²bc - 2a³b² + 4

a)

2

b)

4

c)

5

d)

52

12.

What is the standard form of the polynomial:
9x² + 5x + 27 + 2x³

a)

27 + 5x + 9x² + 2x³

b)

9x² + 5x + 2x³ + 27

c)

9x² + 5x + 27 + 2x³

d)

2x³ + 9x² + 5x + 27

13.

Name and Classify the Polynomial:
x² − 4

a)

quadratic binomial

b)

quadratic monomial

c)

linear binomial

d)

linear monomial

14.

Classify the polynomial by its degree.
x² + 2x³ - 4

a)

A
binomial

b)

B
trinomial

c)

C
quadratic

d)

D
cubic

15.

(x+3)(x+1)

a)

x²+3x+3

b)

2x+4x+3

c)

x²+4x+3

d)

5x + 3

16.

Find the product
(3x + 2)(2x + 4)

a)

6x² + 16x + 8

b)

5x² +11x + 6

c)

5x² + 16x + 6

d)

6x² + 11x + 8

17.

Classify by degree and number of terms.
4m² + 9

a)

Quartic Binomial

b)

Quadratic Binomial

c)

Cubic Trinomial

d)

Quadratic Polynomial of 4 terms

18.

Simplify the product.
2n(n² + 3n + 4)

a)

2n³ + 6n² + 8n

b)

2n³ + 3n + 4

c)

2n³ + 6n + 8

d)

n² + 5n + 4

19.

Simplify the product.
(5h - 3)(3h+7)

a)

15h²-44h+21

b)

15h²-26h+21

c)

15h²+44h-21

d)

15h²+26h-21

20.

Multiply.
(b+3)(b²+2b+1)

a)

b³+6b²+6b+3

b)

b³+5b²+7b+3

c)

4b³+8b²+3b

d)

3b³+6b²+3b

21.

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

a)

-21x⁴ + 3x³ -12x²

b)

7x² - x + 4 (-3x²)

c)

21x⁴+ 3x³+ 12x²

d)

-12x²+ 3x³-21x⁴

22.

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

23.

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

24.

Find the product.
(2x + 3)(x + 5)

a)

2x² + 13x + 15

b)

3x² + x + 8

c)

10x + 15

d)

2x²+ 3x

25.

Find the product.
(2y - 7)(3y + 5)

a)

y²+ 2y + 4

b)

6y² -11y -35

c)

-35 -11y + 6y²

d)

2y²-17y +30

26.

(2x+6)(2x-6)

a)

4x²+24x-36

b)

6x+12

c)

4x²-36

d)

2x+6+2x-6

27.

Find the product.
(x + 7)²

a)

x²+ 7x + 7x + 49

b)

x²+ 7x + 7

c)

7x²+ x + 7

d)

x² + 14x + 49

28.

Multiply (p − 8)²

a)

p ² − 16p − 64

b)

p ² + 16p + 64

c)

p ² − 16p − 8

d)

p ² − 16p + 64

29.

Multiply (3x – 1)(x + 5)

a)

3x² + 4x + 5

b)

3x² + 4x - 5

c)

3x² + 14x + 5

d)

3x² + 14x - 5

30.

Factor the polynomial.
x²-4x-32

a)

(x-8)(x+4)

b)

(x-4)(x-32)

c)

(x+3)(x-4)

d)

x+2)(x+5)

31.

Factor Completely:
x² - 36

a)

(x + 9)(x - 4)

b)

(x - 6)(x - 6)

c)

(x - 9)(x + 4)

d)

(x + 6)(x - 6)

32.

Factor:
x² - 49

a)

(x + 7)(x - 7)

b)

(x + 7)²

c)

(x - 7)²

d)

(x+7)(x-1)

33.

(4x+1)(5x−2)

a)

20x² + 3x − 2

b)

20x² − 11x + 5

c)

20x² − 18x + 2

d)

20x² − 3x − 2

34.

(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

35.

if f(x) = 3x + 2 and g(x) = 11 - 5x,

find (f + g)(x)

a)

-2x + 13

b)

-2x + 9

c)

8x + 13

d)

8x + 9

36.

If g(x) = x² - 4x - 7 and h(x) = 5x² - 8,

find (g - h)(x)

a)

6x² - 4x - 15

b)

-4x² - 4x - 15

c)

-4x² - 4x + 1

d)

-5x² - 4x + 1

37.

if j(x) = (2x + 3) and k(x) = (3x + 2)
find $\left(j\cdot k\right)\left(x\right)$

a)

$5x+5$

b)

$6x^2+6$

c)

$6x^2+6x+6$

d)

$6x^2+13x+6$

38.

Find f(3) + g(2) if f(x)= x+2 and g(x)=5x-1

a)

2

b)

5

c)

9

d)

14

39.

Find (f-g)(2)
if f(x)=4x+10 and g(x)=3x-7

a)

18

b)

-1

c)

19

d)

17

40.

f(n)=x²+1
g(n)=2x-5
Find f(n)-g(n)

a)

x²-2x+6

b)

-x²+2x+4

c)

-x²-2x-6

d)

x²-2x-4

41.

f(x) = 3x² + 7x and g(x) = 2x² - x - 1,
find (f - g)(x).

a)

x² + 8x + 1

b)

x² + 6x - 1

c)

5x² + 8x - 1

d)

x² + 8x -1

42.

Given
f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f + g)(x).

a)

11x² - 1

b)

5x⁴ + 6x² - 1

c)

5x² + 6x - 1

d)

5x² + 8x - 1

43.

f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f - g)(x).

a)

x² + 8x + 1

b)

x² + 6x - 1

c)

5x² + 8x - 1

d)

x² + 8x -1

44.

if 𝑓(𝑥) = 𝑥 + 5; 𝑔(𝑥) = 2𝑥 − 1, find (𝑓 • 𝑔)(3)

a)

40

b)

42

c)

48

d)

44

45.

𝑓(𝑥) = 𝑥 − 8 and 𝑔(𝑥) = 𝑥 + 3, Find 𝑓(𝑥) • 𝑔(𝑥)

a)

𝑥² + 24

b)

𝑥² − 5𝑥 + 24

c)

𝑥² − 5𝑥 − 24

d)

𝑥² + 5𝑥 + 24

46.

Classify by degree of polynomial:
3x³ – 6x

a)

Constant

b)

Linear

c)

Quadratic

d)

Cubic

47.

Classify by number of terms:
2x – 9

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

48.

Classify by degree of polynomial:
2x – 9

a)

Constant

b)

Linear

c)

Quadratic

d)

Cubic

49.

Classify by number of terms:
3x² – 8x + 1

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

50.

Classify by number of terms:
12

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

51.

Classify by degree of polynomial:
12

a)

Constant

b)

Linear

c)

Quadratic

d)

Cubic

52.

When f(x) = 9-3x and g(x) = 5x-7 , find f(x)+g(x).

a)

14x-10

b)

-8x+2

c)

2x+2

d)

2x-2

53.

When f(x) = x²+9 and g(x) = x-9, find f(x)-g(x).

a)

x²+x+9

b)

x²-x+9

c)

x²-x

d)

x²-x+18

54.

h(x) = 3x + 3

g(x) = -4x + 1

Find (h + g)(10)

hint: add h(x) and g(x), then plug in 10

a)

-6

b)

6

c)

82

d)

-72

55.

g(x) = 2x - 5

h(x) = 4x + 5

Find (g - h)(3)

hint: subtract g(x) and h(x), then plug in 3

a)

18

b)

16

c)

-16

d)

28

56.

What are the factors of
$x^2+5x+4$

a)

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

b)

$\left(x-1\right)\left(x-4\right)$

c)

$\left(x-1\right)\left(x+5\right)$

d)

$\left(x+1\right)\left(x+4\right)$

57.

What are the factors of
$2x^2+5x-12$

a)

$\left(x+4\right)\left(2x-3\right)$

b)

$\left(x-3\right)\left(x+8\right)$

c)

$\left(2x+1\right)\left(x-12\right)$

d)

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

58.

factor completely
81m² - 1

a)

not factorable

b)

(m-9)(m+9)

c)

9m(9m-1)

d)

(9m-1)(9m+1)

59.

Factor the GCF
4b⁵+4b³+16b²

a)

4b³(b⁴+b²+4b)

b)

4b³(b⁴+4b+5)

c)

4(b⁵+b³+4b²)

d)

4b²(b³+b+4)

60.

Factor Completely.
$4x^2+24x-64$

a)

$4\left(x+8\right)\left(x-2\right)$

b)

$4(x^2+6x-16)$

c)

$4\left(x^2+24x-16\right)$

d)

$4\left(x-8\right)\left(x+2\right)$

61.

8r³ - 16r²

a)

4r²(2r - 4)

b)

8r²(r - 2)

c)

8(r³ - r²)

d)

4(r³ - 2r²)

62.

Factor completely:

x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

63.

Which of the following is equivalent to:
$2x^2-2x-6$

a)

$2\left(x+3\right)\left(x-1\right)$

b)

$2\left(x+2\right)\left(x-3\right)$

c)

$2\left(x^2-x-3\right)$

d)

$2\left(x^2-2x-6\right)$

64.

Which of the following is equivalent to:
$9x^2+9x-10$

a)

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

b)

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

c)

$\left(3x+5\right)\left(3x+2\right)$

d)

Not Factorable

65.

Which of the following is equivalent to:
$9x^2-6x-8$

a)

$\left(3x+2\right)\left(3x-4\right)$

b)

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

c)

$\left(3x-2\right)\left(3x-4\right)$

d)

$\left(x-1\right)\left(9x+8\right)$

66.

Which of the following is equivalent to:
$3x^2+4x+1$

a)

$\left(7x-10\right)\left(x-8\right)$

b)

Not factorable

c)

$\left(3x+1\right)\left(x+1\right)$

d)

$\left(3x-1\right)\left(x-1\right)$

67.

Which of the following is equivalent to:
$x^2-13x+40$

a)

$\left(x-5\right)\left(x-8\right)$

b)

$\left(x+5\right)\left(x-8\right)$

c)

$\left(x-5\right)\left(x+8\right)$

d)

$\left(x+6\right)\left(x+1\right)$

68.

Factor the trinomial completely. $x^2-x-30$

a)

$\left(x+1\right)\left(x-30\right)$

b)

$\left(x+5\right)\left(x-6\right)$

c)

$\left(x+6\right)\left(x-5\right)$

d)

$prime$

69.

When factored completely, x³ -13x² -30x is

a)

x(x+3)(x-10)

b)

x(x-3)(x-10)

c)

x(x+2)(x-15)

d)

x(x-2)(x+15)

70.

Which expression is equivalent to x⁴ -12x² +36?

a)

(x²-6)(x²-6)

b)

(x²+6)(x²+6)

c)

(6-x²)(6+x²)

d)

(x²+6)(x²-6)

Adding, Subtracting and Multiplying Polynomials Practice

Total questions: 70

Worksheet time: 5hrs 3mins

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