Free Printable Adding, Subtracting, and Multiplying Polynomials

1.

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

a)

-4x +6y + 6z

b)

4x + y + 6z

c)

-4x - y + 6z

d)

-4x + y + 6z

2.

(4x³-5x²+3x)+(-2x³-x²+6x)

a)

2x³-6x²-9x

b)

2x³+6x²+9x

c)

-2x³-6x²+9x

d)

2x³-6x²+9x

3.

A rectangle has width (2x + 3) and length (2x - 4). What is the perimeter of the rectangle?

a)

4x- 12

b)

4x- 1

c)

8x- 2

d)

4x²- 2x - 12

4.

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

5.

Combine like terms to simplify:
(5x + 2) + (4x + 5)

a)

9x -7

b)

-9x-11

c)

9x+7

d)

x+7

6.

Add the polynomials (x-2) and (x²+3)

a)

x²+x+1

b)

x³+5

c)

x³+1

d)

x³-1

7.

Add or Subtract to Simplify:
(4x - 2x³) + (5x³ - 4x + 5)

a)

3x³ + 5

b)

3x³ + 8x + 5

c)

3x² + 5

d)

7x³ + 8x + 5

8.

(4a + 6ab - b) + (-2a - ab + 3b)

a)

2a + 7ab + 2b

b)

6a + 5ab - 2b

c)

6a + 7ab + 4b

d)

2a + 5ab + 2b

9.

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

a)

3y³+ 7y²- 4y + 3

b)

4y² + 3y³ - y + 3

c)

-y⁴ + 2y³-y - 4

d)

4y³+ 3y²-3y + 1

10.

-3(x - 4)

a)

-3x - 12

b)

3x - 12

c)

3x + 12

d)

-3x + 12

11.

Subtract

(4n⁴ - 8n + 4) - (8n² + 4n⁴ + 1)

a)

-8n² - 8n + 3

b)

-7n² - 8n + 3

c)

-6n²- 8n + 3

d)

-7n² - 4n + 3

12.

Subtract

(5x + x² - 4) - (4x - x² + 6)

a)

2x² + x + 2

b)

x + 2

c)

2x² + x - 10

d)

x - 10

13.

Subtract

(x⁵ + x³) - (6x - x³ + 6x⁵)

a)

-5x⁵ + 2x³ - 6x

b)

7x⁵ - 6x

c)

-5x³ + 2x² - 6x

d)

-5x⁵ - 6x

14.

Subtract

(x³-x²+4) - (3x³-2x²+3)

a)

-2x³-3x²+7

b)

-2x³+x²+1

c)

2x³-3x³-1

d)

4x³-3x²+7

15.

Subtract

(2x + 5y) - (3x - 2y)

a)

-x + 3y

b)

-x + 7y

c)

5x + 7y

d)

7xy + 1xy

16.

Subtract

(x³-x²+4) - (3x³-2x²+3)

a)

-2x³-3x²+7

b)

-2x³+x²+1

c)

2x³-3x³-1

d)

4x³-3x²+7

17.

Subtract

(3- 2x + 2x²) - (4x -5 +3x²)

a)

x² + 6x + 8

b)

2x²+ 5x - 7

c)

-x²-6x + 8

d)

-2x² + 11x - 4

18.

Subtract

(x⁵ + x³) - (6x - x³ + 6x⁵)

a)

-5x⁵ + 2x³ - 6x

b)

7x⁵ - 6x

c)

-5x³ + 2x² - 6x

d)

-5x⁵ - 6x

19.

Subtract

(4n⁴ - 8n + 4) - (8n² + 4n⁴ + 1)

a)

-8n² - 8n + 3

b)

-7n² - 8n + 3

c)

-6n²- 8n + 3

d)

-7n² - 4n + 3

20.

Subtract

-4(9 + 3x) - 4(x - 2)

a)

-16x-28

b)

-16x-44

c)

20x - 12

d)

30x - 9

21.

Simplify:
2x ( -2x -3)

a)

-4x - 3

b)

x² - 3

c)

-4x² - 6x

d)

-4x - 6

22.

(x +2)(x + 3)

a)

x² + 5x + 6

b)

x² + x + 6

c)

x² + 5x + 5

d)

x² + 6x + 6

23.

(x + 5)(x + 4)

a)

x² + x + 20

b)

x² + 20x + 9

c)

x² + 9x + 20

d)

x² - 9x + 54

24.

(x + 7)(x + 9)

a)

x² + 63x + 16

b)

x² + 16x + 63

c)

x² + 79

d)

x² + 16x + 2

25.

(x - 5)(x + 1)

a)

x² - 4x - 5

b)

x² + 6x - 5

c)

x² - 5x - 4

d)

x² - 4x - 4

26.

(x - 3)(x +10)

a)

x² - 7x + 13

b)

x² - 6x - 30

c)

x² + 7x - 30

d)

x² + 13x + 30

27.

(2x - 1)(x + 2)

a)

2x² + 3x - 2

b)

2x² - 5x - 2

c)

2x² + 3x + 2

d)

2x² - 5x + 2

28.

(5c-2)(3c²-5c+4)

a)

15c³-31c⁴+30c²-8

b)

15c³-19c²+10c-8

c)

15c³-31c²+30c-8

d)

15c³-31c²+30c+8

29.

(4x+1)(5x−2)

a)

20x² + 3x − 2

b)

20x² − 11x + 5

c)

20x² − 18x + 2

d)

20x² − 3x − 2

30.

(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

31.

(x+2)(x+3)

a)

$x^2+5x+6$

b)

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

c)

5x

32.

(x-4)(x+1)

a)

$x^2-4x+5$

b)

$x^2-4x+1x-4$

c)

$x^2-3x-4$

33.

(x-6)(x-2)

a)

$x^2-6x-8$

b)

$x^2-8x+12$

c)

$x^2-6x-2x+12$

34.

(p-4)(p+2)

a)

$p^2-2p-8$

b)

$p^2-4+2$

c)

$p^2-4p-2p$

35.

(y+5)(y+2)

a)

$y^2+7+9$

b)

$y^2+5x+2$

c)

$y^2+7y+10$

36.

(2x-1)(x+5)

a)

$2x^2+9x-5$

b)

$2x+5x-1x$

c)

$2x^2-1x+5$

37.

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

a)

$9n^2-24n+16$

b)

$3n^2-4x+8$

c)

$n^2-24n+16$

38.

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

a)

$63m^2+2$

b)

$64m^2-4$

c)

$8m^2-2$

39.

(k+4)(5k-1)

a)

$5k^2+4k-4$

b)

$5k^2+19k-4$

c)

$k^2+4k-1$

40.

(x+7)(x+4)

a)

$x^2+4x+7$

b)

$x^2+11x+28$

c)

$7x^2+4+11$

41.

(x+5)(x-6)

a)

$x^2-6x-30$

b)

$x^2-x-30$

c)

$x^2+5x-6$

42.

(x-4)(x-6)

a)

$x^2-10x+24$

b)

$x^2-4x-6$

c)

$x^2+24x-10$

43.

(w-6)(w-9)

a)

$w^2+54w-15$

b)

$w^2-6w+9$

c)

$w^2-15w+54$

44.

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

a)

$4x^2+4x+4$

b)

$2x^2-9x+4$

c)

$4x^2-10x-36$

45.

(4d-5)(2d-3)

a)

$8d^2-22d+15$

b)

$2d^2-5d+15$

c)

$6d^2+15d+8$

46.

(6x-3)(7x-4)

a)

$13x^2-3x+12$

b)

$42x^2-45x+12$

c)

$13x^2-4x+7$

47.

(2x-2)(5x-4)

a)

$10x^2-18x+8$

b)

$7x^2-4x+8$

c)

$10x^2+5x+15$

48.

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

a)

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

b)

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

c)

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

49.

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

a)

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

b)

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

c)

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

50.

(x+6)(x+5)

a)

$x^2+30x+11$

b)

$x^2+11x+30$

c)

$x^2+6x+30$

51.

Simplify.
(p − 6)²

a)

p² + 36

b)

p² + 12p − 36

c)

p² − 12p + 36

d)

p² − 36

52.

Simplify.
(n + 8)²

a)

2n + 16n + 64

b)

n² + 16n + 64

c)

n² + 64

d)

n² + 8n + 64

53.

Simplify.
(x − 8)²

a)

x² + 16x − 64

b)

x² − 16x + 64

c)

x² − 64

d)

x² + 16x + 64

54.

Simplify.
(y − 5)(y + 5)

a)

y² + 25

b)

y² + 10y + 25

c)

y² − 10y + 25

d)

y² − 25

55.

Simplify.
(2b − 6)(2b + 6)

a)

4b² − 24b − 36

b)

4b² − 36

c)

2b² − 36

d)

4b − 36

56.

(x+1)²

a)

x²-1

b)

x²+x+1

c)

x²+1

d)

x²+2x+1

57.

(d + 3)²

a)

d² + 6d + 9

b)

d² + 9d + 9

c)

d² + 6d + 6

d)

d² + 9d + 6

58.

(x - 4)²

a)

x² + 8x - 16

b)

x² - 8x + 16

c)

x² - 16x + 8

d)

x² + 16x - 8

59.

Which special case is this problem

a)

Perfect Square Trinomial

b)

Difference of Two Squares

c)

Neither Special Case

60.

Which special case is this problem

a)

Perfect Square Trinomial

b)

Difference of Two Squares

c)

Neither Special Case

61.

Which special case is this problem

a)

Perfect Square Trinomial

b)

Difference of Two Squares

c)

Neither Special Case

62.

Which special case is this problem

a)

Perfect Square Trinomial

b)

Difference of Two Squares

c)

Neither Special Case

63.

Which special case is this problem

a)

Perfect Square Trinomial

b)

Difference of Two Squares

c)

Neither Special Case

64.

Which special case is this problem

a)

Perfect Square Trinomial

b)

Difference of Two Squares

c)

Neither Special Case

65.

Which special case is this problem

a)

Perfect Square Trinomial

b)

Difference of Two Squares

c)

Neither Special Case

66.

Which special case is this problem

a)

Perfect Square Trinomial

b)

Difference of Two Squares

c)

Neither Special Case

67.

Which special case is this problem

a)

Perfect Square Trinomial

b)

Difference of Two Squares

c)

Neither Special Case

68.

Which special case is this problem

a)

Perfect Square Trinomial

b)

Difference of Two Squares

c)

Neither Special Case

69.

Which special case is this problem

a)

Perfect Square Trinomial

b)

Difference of Two Squares

c)

Neither Special Case

70.

Which special case is this problem

a)

Perfect Square Trinomial

b)

Difference of Two Squares

c)

Neither Special Case

71.

What is the perimeter of this parallelogram?

a)

9x

b)

5x + 4

c)

10x + 8

d)

6x²-9x -45

72.

What is the perimeter of the rectangle?

**Perimeter is the SUM of ALL sides!***

a)

x² + 8x - 5

b)

2x² + 16x - 10

c)

2x² + 10x - 8

d)

6x - 2

73.

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

a)

7y²- 3y + 3

b)

7y⁴ - 3y² + 3

c)

7y² + 3y + 3

d)

7y²- 3y - 3

74.

An airline charges $(20x + 4) for a ticket and $(4x) for a seat upgrade, and $(2x + 1) for premium movies on a flight. Which expression represents the total price you would pay for a seat with an upgrade, and premium movies?

a)

$31x

b)

$24x + 4x + 3x

c)

$24x + 7

d)

$26x + 5

75.

What is the area of a rectangle if the length is $\left(5x+4\right)$ and the width is $\left(4x-4\right)$ ?

a)

$20x^2+36x-16$

b)

$20x^2-4x-16$

c)

$20x^2-16$

d)

$9x^2$

76.

What is the area of a rectangle if the length is $\left(5x-7\right)$ and the width is $\left(5x+6\right)$

a)

$25x^2-5x-42$

b)

$25x^2-42$

c)

$10x^2-1$

d)

$25x^2-65x-42$

77.

What is the area of a square with sides $\left(4x+3\right)$ ?

a)

$16x^2+9$

b)

$16x+12$

c)

$16x^2+24x+9$

d)

$16x^2+14x+9$

78.

What is the area if the length of a rectangle is $\left(2x-1\right)$ and the width is $\left(4x+3\right)$ ?

a)

$8x^2-10x-3$

b)

$6x^2+2$

c)

$8x^2+2x-3$

d)

$8x^2-3$

79.

What is the area of a triangle if the base is $\left(4x+8\right)$ and the height is $\left(4x-5\right)$ ? The formula is $A=\frac{1}{2}bh$ .

a)

$16x^2+12x-40$

b)

$8x^2+6x-20$

c)

$16x^2-40$

d)

$8x^2-20$

80.

What is the area of a circle if the radius is $\left(3x+2\right)$ ? Formula $A=\pi r^2$

a)

$\left(9x^2+12x+4\right)\pi$

b)

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

c)

$\left(6x+4\right)\pi$

Adding, Subtracting, and Multiplying Polynomials

Total questions: 80

Worksheet time: 7hrs 40mins

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