Free Printable Operations on Polynomials

1.

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

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

2.

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

3.

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

4.

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

5.

Find the product:
(3x – 1)(x + 5)

a)

3x² + 4x + 5

b)

3x² + 4x - 5

c)

3x² + 14x + 5

d)

3x² + 14x - 5

6.

Simplify:
(3x - 5) ( 4x² - 2x - 3)

a)

12x³ - 26x² - 25x + 15

b)

12x³ - 20x² - 5x + 15

c)

12x³ - 20x² - 6x + 15

d)

12x³ - 26x² + x + 15

7.

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

8.

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

9.

Simplify the expression.
x³(2x²+3x)

a)

2x⁵+3x⁴

b)

2x⁶+3x³

c)

5x⁹

d)

5x

10.

Find the difference.
(7p + 4p³ - 8) - (-3p²+ 2 - 9p)

a)

-3p²+ 4p³ -15 + 9

b)

3p³ + 4p² - p + 3

c)

4p³ -3p² +16p -10

d)

4p³ +3p² + 16p + 10

11.

^simplify 5x³2x²

a)

10x⁵

b)

3x

c)

10x⁶

d)

7x⁵

12.

Simplify the following:
(x²y)⁵

a)

x⁷y⁵

b)

x²y⁵

c)

x¹⁰y⁵

d)

x⁵y⁵

13.

Simplify the expression

a)

x²/2

b)

2/x¹⁴

c)

2x¹⁴

d)

2/x²

14.

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

a)

-21x⁴ + 3x³ -12x²

b)

7x² - x + 4 (-3x²)

c)

21x⁴+ 3x³+ 12x²

d)

-12x²+ 3x³-21x⁴

15.

Find the product:

(2x + 7)²

a)

4x²+ 49

b)

4x²+ 28x + 49

c)

4x² + 14x + 49

16.

Simplify:
(3x - 5) ( 4x² - 2x - 3)

a)

12x³ - 26x² - 25x + 15

b)

12x³ - 20x² - 5x + 15

c)

12x³ - 20x² - 6x + 15

d)

12x³ - 26x² + x + 15

17.

Find the product:
(5n-8)(5n+8)

a)

25n²-64

b)

10n²

c)

5n²+16

d)

16

18.

The measure of two side of a triangle is x²+ 2x. If the perimeter is 4x²+ x, what is the measure of the third side?

a)

3x²- x

b)

4x²+ 2x

c)

3x² + 3x

d)

3x² + 2x

19.

Which expression is equivalent to:
(2x²+5x-7)(x-2)?

a)

2x³ - x² + 17x -14

b)

2x³ + 9x² + 3x +14

c)

2x³ + x² + 3x +14

d)

2x³ + x² - 17x +14

20.

Which of the following expressions represents the quotient of $\frac{8x^3+10x^2-4x+6}{x+1}$

a)

$8x^2+2x-6+\frac{12}{x+1}$

b)

$8x^2+2x-6-\frac{9}{x+1}$

c)

$8x^2+18x+14+\frac{11}{x+1}$

d)

$8x^2+18x+14-\frac{17}{x+1}$

21.

How do we write the following polynomial in standard form: 3x³ + 6x² - x - 2x⁵ + 4x⁴

a)

-2x⁵+ 4x⁴+ 3x³ + 6x²- x

b)

10x¹⁵

c)

-x + 6x² + 3x³ + 4x⁴ - 2x⁵

22.

Factor completely: x⁴- 81

a)

(x²+ 9) (x + 3) (x - 3)

b)

(x² + 9) ( x² - 9)

c)

(x + 3)² (x - 3)²

23.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect, and error occurs on the 2nd line!

c)

This is incorrect, and the error occurs on the 4th line!

d)

This is incorrect, and the error occurs on the 3rd line!

24.

Which term must be inserted in the dividend before you begin long division?

$\left(2x^3+5x^2+9\right)\div\left(x+3\right)$

a)

$0x^4$

b)

$0x^3$

c)

$0x^2$

d)

$0x$

25.

For synthetic division, what would be the number in the left hand box?

a)

0

b)

-2

c)

2

d)

3

26.

Classify by degree of polynomial:
-2x² – x

a)

Constant

b)

Linear

c)

Quadratic

d)

Cubic

27.

Classify the following polynomial

a)

quadratic trinomial

b)

cubic binomial

c)

constant monomial

d)

quadratic binomial

28.

What is the end behavior for the graph?

a)

x → ⁻∞, y→ ⁻∞ and

x→ ∞, y→ ⁻∞

b)

x → ⁻∞, y→ ∞ and

x→ ∞, y→ ∞

c)

x → ⁻∞, y→ ⁻∞ and

x→ ∞, y→ ∞

d)

x → ⁻∞, y→ ∞ and

x→ ∞, y→ ⁻∞

29.

Which of the following correctly identifies the End Behavior?

a)

b)

c)

d)

30.

What is the increasing interval(s) on the function shown?

a)

$\left(-\infty,\ -15\right)\ and\ \left(9,\ -15\right)$

b)

$\left(-2,\ 9\right)\ and\ \left(2,\ \infty\right)$

c)

$\left(-\infty,\ -2\right)\ and\ \left(0,\ 2\right)$

d)

$\left(-2,\ 0\right)\ and\ \left(2,\ \infty\right)$

31.

What is the decreasing interval(s) on the function shown?

a)

$\left(-\infty,\ -15\right)\ and\ \left(9,\ -15\right)$

b)

$\left(-2,\ 9\right)\ and\ \left(2,\ \infty\right)$

c)

$\left(-\infty,\ -2\right)\ and\ \left(0,\ 2\right)$

d)

$\left(-2,\ 0\right)\ and\ \left(2,\ \infty\right)$

32.

a)

(0, 4)

b)

(2, 0)

c)

(0, 2)

d)

(-1, 0)

33.

Which of the following may have an outcome that is not a polynomial?

a)

the addition of two polynomials

b)

the multiplication of two polynomials

c)

the subtraction of two polynomials

d)

the division of two polynomials

34.

What is the correct expansion of $\left(x+y\right)^5$

a)

$x^5+4x^4y+6x^3y^2+4x^2y^4+y^5$

b)

$x^5+5x^4y+10x^3y^2+5x^2y^4+y^5$

c)

$x^5+4x^4y+6x^3y^2+6x^2y^3+4xy^4+y^5$

d)

$x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5$

35.

Which is the result of dividing $4x^3-13x^2+x+6$ by $x-3$ ?

a)

$4x^2-x-2$

b)

$4x^2-x-2+\frac{3}{x-3}$

c)

$4x^2+49x+228$

d)

$4x^2-25x+\frac{302}{x-3}$

36.

This table contains the order pairs (x, y) of a function.

(-1, -2.5), (0, -2), (1, -1), (2, 1), and (3, 5).

Which of the following is not a point on the inverse of this function?

a)

(-2, 0)

b)

(-1, -1)

c)

(1, 2)

d)

(5, 3)

37.

Which of the following is the inverse of $f\left(x\right)=3x+4$ ?

a)

$f^{-1}\left(x\right)=\frac{x-3}{4}$

b)

$f^{-1}\left(x\right)=\frac{x-4}{3}$

c)

$f^{-1}\left(x\right)=\frac{x+3}{4}$

d)

$f^{-1}\left(x\right)=x+4$

38.

Which choice below describes two functions that are inverses of each other?

a)

$f\left(x\right)=\frac{2}{x-2},\ g\left(x\right)=\frac{x-2}{2}$

b)

$f\left(x\right)=\frac{2}{x-2},\ g\left(x\right)=\frac{2}{x+2}$

c)

$f\left(x\right)=\frac{2}{x},\ g\left(x\right)=\frac{2}{x}$

d)

$f\left(x\right)=\frac{2}{x},\ g\left(x\right)=\frac{1}{2}x$

39.

Which of the following is not a true statement?

a)

the quantity i is defined as $\sqrt{-1}$

b)

In a complex number a + bi, a and b are real numbers

c)

The number 4 +2i and 2 + 4i are complex conjugates

d)

Every complex number has a complex conjugate.

40.

Which of the following is not always equal to a polynomial?

a)

sum of polynomials

b)

difference of polynomials

c)

product of polynomials

d)

quotient of polynomials

Operations on Polynomials

Total questions: 40

Worksheet time: 40mins

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