Free Printable All Operations with Polynomials

1.

$\left(n^3-3n-5n^2\right)+\left(n^2+3+2n^3\right)$

a)

$-n^3-4n^2+n+3$

b)

$3n^3-4n^2+n+3$

c)

$2n^3-4n^2+n+3$

d)

$3n^3-4n^2-3n+3$

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.

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

a)

$10x^3-5x^2-8$

b)

$10x^3-10x^2-8$

c)

$10x^3-10x^2-3$

d)

$10x^3-10x^2-7$

4.

$\left(3p+2p^3-5p^2\right)-\left(p^2-5p-2p^3\right)+\left(p^2+4p^3+5p\right)$

a)

$11p^3-4p^2+13p$

b)

$8p^3-5p^2+13p$

c)

$9p^3-4p^2+13p$

d)

$9p^3-5p^2+13p$

5.

(3x² + 4x - 2) - (5x + 7)

a)

3x² - x - 9

b)

2x² - 9

c)

3x² + 9x - 5

d)

3x² - x + 5

6.

(4x - 1)(5x−2)

a)

20x² + 3x − 2

b)

20x² − 11x + 5

c)

20x² − 13x + 2

d)

20x² − 3x − 2

7.

$(2x−5)(4x^2−7x+3)$

a)

$8x^3−15$

b)

$4x^3−14x^2−15$

c)

$8x^3−14x^2+6x−5$

d)

$8x^3−34x^2+41x−15$

8.

What does FOIL stand for?

a)

Failing Only in Latin

b)

Farming Only in Lakewood

c)

First Outside Inside Last

d)

Fresh Only in Lakes

9.

Find the product.
-3x²( 7x²- x + 4)

a)

-21x⁴ + 3x³ -12x²

b)

7x² - x + 4 (-3x²)

c)

21x⁴+ 3x³+ 12x²

d)

-12x²+ 3x³-21x⁴

10.

Which polynomial is written in standard form?

a)

-3x + 8x² + 9x³ - 11

b)

9x³ + 8x²- 3x - 11

c)

8x²+ 9x³ -11 - 3x

d)

-11 - 3x + 8x² + 9x³

11.

Classify by number of terms:
3x³ – 6x

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

12.

Classify by degree of polynomial:
3x³ – 6x

a)

Constant

b)

Linear

c)

Quadratic

d)

Cubic

13.

Classify by number of terms:
2x – 9

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

14.

Classify by degree of polynomial:
2x – 9

a)

Constant

b)

Linear

c)

Quadratic

d)

Cubic

15.

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

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

16.

Classify by degree and number of terms:

3x³ – 6x

a)

Quadratic Binomial

b)

Cubic Binomial

c)

Cubic Trinomial

d)

4th degree Binomial

17.

Classify the polynomial by degree and number of terms:

3x² – 8x + 1

a)

Cubic Trinomial

b)

Cubic Binomial

c)

Quadratic Trinomial

d)

Quadratic Binomial

18.

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

a)

0

b)

1

c)

2

d)

3

19.

If you were dividing x⁶ + 4x³ + 2, how many 0's would you need when setting up the top row of your synthetic division?

a)

0

b)

2

c)

4

d)

6

20.

What should be the order of the polynomial coefficients if
(3x - 4x³ + 6x⁴ + 1) / (x + 3)

a)

3 0 -4 6 1

b)

6 -4 3 1 0

c)

6 -4 0 3 1

d)

-6 4 0 -3 -1

21.

What is the proper way to write the answer for the following problem?

a)

2x³-x²-25x+12

b)

2x⁴-x³-25x²-12x+0

c)

2x³-x²-25x-12

d)

2x⁴-x³-25x²-12x-0

22.

(2x³ + 7x² - 6x - 8) ÷ (x + 4)

a)

2x² - x - 2

b)

2x³ - x² - 2x

c)

2x² + 15x + 54 + 208/x+4

d)

2x³ + 15x² + 54x + 208

23.

Divide using synthetic division
(2x³ + 4x² - 5) by (x + 3).

a)

2x² + 2x - 4 R(-12)

b)

2x² - 2x + 6 R(-23)

c)

2x² - 2x + 8 R(-20)

d)

2x² - 4x + 1 R0

24.

$\frac{20x^2}{5x}$

a)

$15x$

b)

$4x$

c)

$15x^2$

d)

$25x$

25.

$\left(14d^3-21d^8\right)\div\ 7d^2$

a)

$7d-21d^6$

b)

$7d^{1.5}-14d^4$

c)

$2d-3d^6$

d)

$2d^{1.5}-3d^4$

26.

$\frac{\left(8x^4+6x^3-10x^2\right)}{2x^2}$

a)

$4x^2+3x-5$

b)

$4x^2+3x^{1.5}-5x$

c)

$6x^2+4x-12$

d)

$6x^2+4x^{1.5}-12x$

27.

$\frac{\left(-18x^5-12x^3-6x^2\right)}{-3x}$

a)

$-15x^4-9x^2-3x$

b)

$-6x^4-4x^2-2x$

c)

$6x^4+4x^2+2x$

d)

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

All Operations with Polynomials

Total questions: 27

Worksheet time: 1hrs 6mins

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