Free Printable Polynomials and factoring

1.

Factor Completely: 5x³+20x²+20x

a)

5x(x+2)(x+2)

b)

5x(x²+4x+4)

c)

5x(x+2)(x+4)

d)

Cannot Be Factored

2.

Factor Completely: x⁴-16

a)

(x²+4)(x²-4)

b)

(x²+4)(x+2)(x-2)

c)

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

d)

Cannot Be Factored

3.

Factor Completely: 2x³+5x²+6x+15

a)

x(2x²+5x+6)+15

b)

(x²+5)(2x+3)

c)

(x²+3)(2x+5)

d)

Cannot Be Factored

4.

Factor Completely: 3x²+7x+2

a)

(3x+1)(x+2)

b)

(x+6)(x+1)

c)

(3x-1)(x-2)

d)

Cannot Be Factored

5.

Factor Completely: x²+4x-21

a)

(x+7)(x-3)

b)

(x-7)(x+3)

c)

(x-7)(x-3)

d)

Cannot Be Factored

6.

Factor completely: 16x²-1

a)

(4x-1)(4x-1)

b)

(8x+1)(8x-1)

c)

(4x+1)(4x-1)

d)

Cannot Be Factored

7.

Factor completely: x²-4

a)

(x+4)(x-4)

b)

(x+2)(x-2)

c)

(x-2)(x-2)

d)

Cannot Be Factored

8.

Factor by finding the GCF: 3x⁴+12x²

a)

3(x⁴+4x²)

b)

3x(x³+4x)

c)

3x³(x+4)

d)

3x²(x²+4)

9.

Multiply: (3x-1)(2x+4)

a)

5x²-10x-4

b)

6x²+14x+4

c)

6x²+10x-4

d)

6x²+14x-4

10.

Multiply: (x+3)(x-1)

a)

x²+2x-3

b)

x²-3x+2

c)

x²+4x+3

d)

x²+3x+4

11.

Classify the polynomial 3x²-4x+2

a)

Cubic Binomial

b)

Quadratic Trinomial

c)

Cubic Trinomial

d)

Quadratic Polynomial

12.

(5x+1)(x+4)

a)

5x² + 19x − 4

b)

5x² + 21x + 4

c)

5x² + 4

d)

5x² − 19x − 4

13.

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

a)

7x - 7x + 5x²

b)

5x²+ 2x - 2

c)

5x²

d)

5x² + 6x + 8

14.

Find the area of the rectangle.

a)

8x² + 14x + 6

b)

12x + 10

c)

8x² + 6

d)

6x² + 14x + 6

15.

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

16.

Simplify:
2x ( -2x -3)

a)

-4x - 3

b)

x² - 3

c)

-4x² - 6x

d)

-4x - 6

17.

The formula P = 2(l) + 2(w) can be used to find the perimeter of a rectangle. Which expression represents the perimeter of the rectangle shown?

a)

1/2x² + 18x - 14

b)

x² + 18x - 14

c)

x² + 10x + 14

d)

19x - 4

18.

Which expression is equivalent to 6x² - 13x + 6?

a)

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

b)

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

c)

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

d)

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

19.

If possible, factor completely.

75x² - 48

a)

3(5x + 4)(5x - 4)

b)

3(25x² - 16)

c)

3(5x - 4)²

d)

Not factorable

20.

What is the term classification of the following polynomial?
x³-7x²+3

a)

monomial

b)

binomial

c)

trinomial

d)

polynomial

21.

The following polynomial is written in standard form:
7x³ - 11x² + 8x - 5

a)

True

b)

False

22.

Classify by the DEGREE:
3x - 2

a)

Degree of 1

b)

Degree of 2

c)

Degree of 3

d)

Degree of 4

23.

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

a)

Degree of 1

b)

Degree of 2

c)

Degree of 3

d)

Degree of 4

24.

What is the Degree of the Polynomial?

5x³ - 6x + 1

a)

Linear

b)

Quadratic

c)

Cubic

d)

Quartic

25.

What is the leading coefficient?
f(x)=5x²+3x³-2x+1

a)

5

b)

3

c)

-2

d)

1

26.

Which of the following is a 5th degree trinomial with a leading coefficient of -2?

a)

-2x⁵ + 3x - 1

b)

5x^-2 +3x - 1

c)

-2x⁵ + 3x⁴ + 2x³ + x² - 10

d)

2x + 5

27.

What is the constant in the polynomial x²-2x+5?

a)

1

b)

2

c)

5

d)

0

28.

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

29.

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

30.

(3x² + 4x - 2) - (5x + 7)

a)

3x² - x - 9

b)

2x² - 9

c)

3x² + 9x - 5

d)

3x² - x + 5

31.

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

32.

What is the Perimeter?

a)

3x - 3 inches

b)

6x - 6 inches

c)

3x - 6 inches

d)

6x - 3 inches

33.

6v(2v + 3)

a)

12v+18

b)

15v² + 8v

c)

12v² + 18v

d)

12v² + 18v²

34.

2x³(x²−2x − 3)

a)

2x⁶- 4x³ - 6x³

b)

2x⁵−4x⁴ − 6x³

c)

-2x⁵−4x⁴ − 6x³

d)

-2x⁶−4x³ − 6x³

35.

(2n + 2)(6n + 1)

a)

12n + 2

b)

12n² + 2

c)

12n² + 12n + 2

d)

12n² + 14n + 2

36.

(x − 3)(6x − 2)

a)

6x² − 20x + 6

b)

6x² + 20x - 6

c)

6x² +6

d)

6x + 6

37.

(4p − 1)(4p - 1)

a)

16p² + 1

b)

16p² − 1

c)

16p² − 8p + 1

d)

16p² + 8p + 1

38.

(x+10)(x-10)

a)

x² - 100

b)

x² + 100

c)

x² + 20x - 100

d)

x² -20x + 100

39.

What is the GCF? 5x²+20x

a)

5

b)

x

c)

5x

d)

20x

40.

What is the GCF? 3x²-2x

a)

3

b)

3x

c)

x

d)

2

41.

Factor:
10x + 15

a)

100x + 150

b)

10(x + 5)

c)

1(10x + 15)

d)

5(2x + 3)

42.

Factor by using GCF:
8n³ + 2n²

a)

2n²(4n-1)

b)

2n²(4n + 1)

c)

n²(8n+2)

d)

3n(4n+1)

43.

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)

44.

Find the slope

a)

-5/3

b)

-3/5

c)

5/3

d)

3/5

45.

Find the slope:

a)

3/4

b)

4/3

c)

-3/4

d)

-4/3

46.

The slopes of parallel lines are...

a)

the same

b)

opposite

c)

always different

47.

Slope is know as rise/

a)

run

b)

fall

c)

none

d)

rise

48.

Find the slope of the line.

a)

-2

b)

2

c)

-1

d)

1

49.

Find the slope of the line that passes through:
(6,7) and (4,2)

a)

2/5

b)

-5/2

c)

5/2

d)

-1/2

50.

Find the slope of the line that passes through:
(2, 4) and (6, 12)

a)

1/2

b)

-1/2

c)

2

d)

-2

51.

Find the slope of the line that passes through:
(10, 1) and (5, 2)

a)

1/5

b)

-1/5

c)

5

d)

-5

52.

What is the slope represented in the table?

a)

slope: $\frac{1}{2}$

b)

slope: $2$

c)

slope: $-\frac{1}{2}$

d)

slope: $-2$

53.

What is the Slope represented in this table?

a)

slope: $-\frac{1}{4}$

b)

slope: $-4$

c)

slope: $\frac{1}{4}$

d)

slope: $4$

54.

The y-intercept is (a) and the slope is (b)

Choose from the below words

(0,-3)

$\frac{3}{4}$

(-3,0)

(4,0)

(0,4)

$\frac{4}{3}$

$-\frac{3}{4}$

$-\frac{4}{3}$

55.

Given: $y=-\frac{1}{3}x+5$ , the slope is (a) and the y-intercept is (b)

Choose from the below words

$-\frac{1}{3}$

5

-5

$\frac{1}{3}$

$\frac{3}{1}$

$-\frac{3}{1}$

56.

Given: $y=\frac{3}{5}x$ , the slope is (a) and the y-intercept is (b)

Choose from the below words

$\frac{3}{5}$

0

1

$\frac{5}{3}$

$-\frac{3}{5}$

$-\frac{5}{3}$

57.

Given: $y=4$ , the slope is (a) and the y-intercept is (b)

Choose from the below words

$0$

$4$

$\frac{1}{4}$

$\frac{4}{1}$

$-4$

$-1$

$1$

58.

Which graph represents the function: $y=-\frac{1}{2}x-2$

a)

b)

59.

Which graph represents the function: $y=\frac{3}{2}x+3$

a)

b)

c)

d)

60.

What equation is graphed?

a)

$y=5x+1$

b)

$y=-5x+1$

c)

$y=\frac{1}{5}x+1$

d)

$y=-\frac{1}{5}x+1$

61.

Write the equation of the line in Slope-Intercept Form. ( $y=mx+b$ )

62.

Write the equation of the line in Slope-Intercept Form. ( $y=mx+b$ )

Polynomials and factoring

Total questions: 62

Worksheet time: 2hrs 43mins

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