Free Printable Polynomials

1.

Classify by number of terms:

$3x^3-6x$

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

2.

Classify by number of terms:

$3x^2\ +\ 8x\ -\ 1$

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

3.

Classify: $2n^3$

a)

Monomial

b)

Binomial

c)

Trinomial

d)

Polynomial

4.

Classify by the DEGREE:
4x³ - 5x² + 2x - 1

a)

1

b)

2

c)

3

d)

4

5.

What is the degree of the polynomial 17x + 4

a)

0

b)

1

c)

2

d)

3

6.

2) Degree of

2x^2+50

is _____

a)

50

b)

2

c)

4

d)

1

7.

7) Degree of 10 is ______

a)

10

b)

1

c)

0

d)

Undefined

8.

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

9.

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

a)

-4x +6y + 6z

b)

4x + y + 6z

c)

-4x - y + 6z

d)

-4x + y + 6z

10.

Simplify (4x³- 5x²+ 3x) + (-2x³- x²+ 6x)

a)

2x³- 6x²- 9x

b)

2x³+ 6x²+ 9x

c)

-2x³- 6x²+ 9x

d)

2x³- 6x²+ 9x

11.

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

12.

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

a)

-4x +6y + 6z

b)

4x + y + 6z

c)

-4x - y + 6z

d)

-4x + y + 6z

13.

Simplify (4x³- 5x²+ 3x) + (-2x³- x²+ 6x)

a)

2x³- 6x²- 9x

b)

2x³+ 6x²+ 9x

c)

-2x³- 6x²+ 9x

d)

2x³- 6x²+ 9x

14.

Simplify (4x³+ 5x²+ 3x) + (-2x³ +1x²+ 6x)

a)

2x³- 6x²- 9x

b)

2x³+ 6x²+ 9x

c)

-2x³- 6x²+ 9x

d)

2x³- 6x²+ 9x

15.

Simplify (-8v⁴ + 4v³ + 3v) + (- 8v⁴+ 4v - 7)

a)

-17v⁴ + 4v³ + 2v - 7

b)

-16v⁴ + 4v³ + 10v - 7

c)

-16v⁴ + 4v³ + 7v - 7

d)

-16v⁴ + 4v³ + 2v - 7

16.

Combine (3x - 4) + (12x + 10)

a)

x - 12

b)

15x + 6

c)

36x + 40

d)

17x + 9,000

17.

Simplify (9x + 17) + (19x - 27)

a)

28x + 44

b)

28x - 10

c)

-28x + 10

d)

-171x - 459

18.

Simplify (2x² + 5x - 7) + ( 3 - 4x² + 6x)

a)

2x²+ 3x +1

b)

-2x²- 11x -4

c)

2x²+ 5x -7

d)

-2x² + 11x -4

19.

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

a)

3x + 5y

b)

5x + 3y

c)

5x + 7y

d)

7xy + 1xy

20.

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

21.

Add or Subtract to Simplify:
(5x + x² - 4) - (4x - x² + 6)

a)

2x² + x + 2

b)

x + 2

c)

2x² + x - 10

d)

x - 10

22.

Add or Subtract to Simplify:
(x⁵ + x³) - (6x - x³ + 6x⁵)

a)

-5x⁵ + 2x³ - 6x

b)

7x⁵ - 6x

c)

-5x³ + 2x² - 6x

d)

-5x⁵ - 6x

23.

Simplify (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

24.

Add or Subtract to Simplify:
(4n⁴ - 8n + 4) - (8n² + 4n⁴ + 1)

a)

-8n² - 8n + 3

b)

-7n² - 8n + 3

c)

-6n²- 8n + 3

d)

-7n² - 4n + 3

25.

Add or Subtract to Simplify:
(6b³ + 6 - b⁴) - (8b³ - 6b⁴ + 2)

a)

4b⁴ - 2b³ + 7

b)

5b⁴ - 2b³ + 4

c)

b⁴ - 2b³ + 7

d)

5b⁴ - 2b³ + 7

26.

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

27.

Simplify each expression.
(6b³ + 6 - b⁴) - (8b³ - 6b⁴ + 2)

a)

4b⁴ - 2b³ + 7

b)

5b⁴ - 2b³ + 4

c)

b⁴ - 2b³ + 7

d)

5b⁴ - 2b³ + 7

28.

Add or Subtract to Simplify:
(4n⁴ - 8n + 4) - (8n² + 4n⁴ + 1)

a)

-8n² - 8n + 3

b)

-7n² - 8n + 3

c)

-6n²- 8n + 3

d)

-7n² - 4n + 3

29.

Match the following:

a)

Monomial

1.

( $-2x$ )

b)

Binomial

2.

( $3x^2+7$ )

c)

Trinomial

3.

( $5x^2+7x-10$ )

d)

Polynomial

4.

( $8x^4+7x^2+3x-9$ )

30.

What is the perimeter of the rectangle?

a)

x²+8x-5

b)

2x²+16x-10

c)

2x²+10x-8

d)

6x-2

31.

Find the product:

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

a)

6x² + 16x + 8

b)

5x² +11x + 6

c)

5x² + 16x + 6

d)

6x² + 11x + 8

32.

Find the product.

$\left(3x\ -\ 1\right)\left(x\ +\ 5\right)$

a)

3x² + 4x + 5

b)

3x² + 4x - 5

c)

3x² + 14x + 5

d)

3x² + 14x - 5

33.

Find the product: $\left(n\ -\ 5\right)\left(n\ -\ 1\right)$

a)

n² - 5n + 5

b)

n² - 6n + 5

c)

n²+ 5

d)

n² + 6n + 5

34.

Find the product.

$\left(p\ -\ 8\right)^2$

a)

p ² − 16p − 64

b)

p ² + 16p + 64

c)

p ² − 16p − 8

d)

p ² − 16p + 64

35.

Find the product:

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

a)

$2x^2-5x+4$

b)

$2x^2+3x+14$

c)

$2x^2-3x-14$

d)

$x^2+3x-14$

36.

What is the area of this rectangle?

a)

48

b)

$8x^2+14x+6$

c)

$8x^2+x+5$

d)

$2x^2+6x+8$

37.

Find the product:

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

a)

x²+16

b)

x²-16

c)

x²+8x+16

d)

x²+8x-16

38.

Find the product:

$\left(7r\ -\ 6\right)\left(7r\ +\ 6\right)$

a)

49r²+ 36

b)

49r²- 36

c)

49r²+ 84r + 36

d)

49r²+ 42r + 36

39.

Find the product.

(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

40.

Find the product:
$\left(8x-7\right)\left(2-6x+9x^2\right)$

a)

$9x^3+14x^2-7x+14$

b)

$72x^3-111x^2+58x-14$

c)

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

d)

$3x^3-2x^2+7x-9$

41.

Find the product:
$\left(4x^2+14x-6\right)\left(11-3x\right)$

a)

$x^3-14x^2-6x+1$

b)

$12x^3+86x^2+172x-6$

c)

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

d)

$-12x^3+2x^2+172x-66$

42.

Find the product:
$\left(x+1\right)\left(x^2-4x-21\right)$

a)

$x^3-3x^2-25x-21$

b)

$x^3+3x^2+25x+21$

c)

$-x^3-3x^2-25x-21$

d)

$x^4-3x^3-25x^2-21x$

43.

Factor by grouping:
5n³-10n²+3n-6

a)

(5n²+3)(n-2)

b)

(5n²-3)(n-2)

c)

(5n³+3)(n-2)

d)

10n(n²-6)

44.

Factor by grouping:
x³+7x²-2x-14

a)

(x²-2)(x-7)

b)

(x²+2)(x-7)

c)

(x²+2)(x+7)

d)

(x²-2)(x+7)

45.

Factor by grouping:
4p³+8p²+3p+6

a)

(2p²+3)(p+2)

b)

(2p²+6)(p+4)

c)

(4p²+3)(p+2)

d)

(4p²+8p)(3p+6)

46.

Factor by grouping
x³ - 4x² -4x + 16

a)

(x+4)(x+2)

b)

(x-4)(x² -4)

c)

(x+4)(x² -4)

d)

(x-4)(x-2)

47.

Factor
r² -16r + 60

a)

(r - 15)(r + 4)

b)

(r - 6)(r + 10)

c)

(r - 6)(r - 10)

d)

(r +30)(r - 2)

48.

Factor
n² + 16n + 63

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

49.

Factor
k²+7k+10

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

50.

Factor
k² -2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

51.

Factor:
x² + 7x + 6

a)

(x + 6) (x + 1)

b)

(x + 3) (x + 2)

c)

(x + 4) ( x + 3)

d)

(x - 6) ( x -1)

52.

Factor:
x² - 10x + 9

a)

(x - 9) (x - 1)

b)

(x + 3) (x - 3)

c)

(x + 9) (x - 1)

d)

Prim polynomial

53.

Factor Completely: 6x² + 5x - 6

a)

6(x + 1)(x - 6)

b)

(6x + 6)(x - 1)

c)

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

d)

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

54.

Factor:
4h² - 17h + 4

a)

(2h - 2)²

b)

4(h + 4)(h + 1)

c)

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

d)

(h - 4)(4h - 1)

55.

Factor completely.
2n² + 13n + 15

a)

(5n - 9)(n - 3)

b)

(3n + 7)(n + 4)

c)

(2n + 3)(n + 5)

d)

Not factorable

56.

Factor completely.
5x² - 13x + 6

a)

(x - 3)(5x - 2)

b)

(5x - 3)(x - 2)

c)

5(x - 3)(x + 2)

d)

Not factorable

57.

Factor:
2m² + 3m - 9

a)

2(m + 3)(m - 3)

b)

(2m - 3)²

c)

(m + 3)(2m - 3)

d)

(2m + 3)(m - 3)

58.

What is the Greatest Common Factor of the following polynomial?
12t³ + 30t² + 48t

a)

12t

b)

6t³

c)

6t

d)

12t³

59.

Factor completely 5x² + 20

a)

5(x + 4)

b)

5x(x + 4)

c)

5(x² + 4)

d)

5x²(x + 4)

60.

6x²y - 18xy²

a)

6(x - 3y)

b)

6xy(x - 3y)

c)

6xy²(x - 3)

d)

6x²y(3y - 1)

61.

Factor -9x + 33 using the GCF

a)

3 (-3x + 11)

b)

-9 (x + 4)

c)

-3 (3x + 11)

d)

9 ( -x + 4)

62.

Factor using the GCF: 3x³+ 9x²- 15x

a)

x(3x² + 9x - 15)

b)

3x(x² + 3x - 5)

c)

3x(x² - 9x + 15)

d)

x(3x² -9x + 15)

63.

Factor by using GCF:
10x² + 15x-5

a)

25(10x³+45x-15)

b)

5(2x³ + 3x²-x)

c)

x(10x³+15x-5)

d)

5(2x²+3x-1)

64.

Factor:
2n²+16n+12

a)

2n(n²+24n+6)

b)

2(n²+8n+6)

c)

2n(n²+8n+6)

d)

3(n²+8n+6)

65.

Factor:
80x⁵-70x²-60x⁷

a)

2x²(80x³-70-60x⁶)

b)

10x²(80x⁴-70x-60x⁶)

c)

10x²(8x³-7-6x⁵)

d)

3x²(80x³-40-60x⁵)

66.

Factor by using GCF:
8n³ + 2n²

a)

2n²(4n-1)

b)

2n²(4n + 1)

c)

n²(8n+2)

d)

3n(4n+1)

67.

Factor
4b⁵+4b³+16b²

a)

4b³(b⁴+b²+4b)

b)

4b³(b⁴+4b+5)

c)

4(b⁵+b³+4b²)

d)

4b²(b³+b+4)

68.

Solve by factoring: x² = 7x + 18

a)

-7 and -18

b)

9 and 2

c)

9 and -2

d)

2 and 7

69.

Solve by factoring: 2x²+ 7x + 6 = 0

a)

x= 3/2 and x = 2

b)

x = -3/2 and x = -2

c)

x = 6 and x = 7

d)

x = -6 and x = -7

70.

Solve for x:

(x-5)(x+6)=0

a)

{5,5 }

b)

{ -5,-5 }

c)

{ -5,-6 }

d)

{5,-6 }

71.

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

a)

Plug in zero for x

b)

Solve for x

c)

FOIL

d)

Set each binomial factor equal to zero

72.

What are the factors AND solutions of x² + 2x – 3 = 0

a)

(x - 2)(x + 1); x=2, x=-1

b)

(x + 1)(x - 3); x=-1, x=3

c)

(x + 2)(x - 1); x=-2, x=1

d)

(x - 1)(x + 3); x=1, x=-3

73.

Solve by factoring:
x² - 9x = 0

a)

9

b)

0, 9

c)

-9, 0

d)

-9

74.

What property would you use to solve the following?
(x-3)(x+2)=0

a)

Commutative Property

b)

Associative Property

c)

Zero Product Property

d)

Inverse Property

75.

Solve using Zero-Product Property.

(2x - 2)(5x + 5) = 0

a)

x = -1

b)

x = -1 or x = 1

c)

x = 1

d)

x = -2 or x = 5

76.

What should you do first in solving this equation?
x² + 6x - 13 = 3

a)

Get factored form

b)

Find two numbers which add to make 6 and multiply to make -13

c)

Make it equal 0 by subtracting 3 on each side

d)

Type it all in a calculator.

77.

Solve by factoring.

n² - 2n = 0

a)

n = 2 and 0

b)

n = -2 and 0

c)

n = 2

d)

n = 0

78.

Solve: $20x=5x^2+20$ by factoring

a)

$x=0$ and $x=2$

b)

$x=-2$

c)

$x=2$

d)

$x=2$ and $x=-2$

Polynomials

Total questions: 78

Worksheet time: 6hrs 54mins

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