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Dividing Polynomials

In this worksheet, students divide polynomial expressions by the given term.

'Dividing Polynomials' worksheet

Key stage:  KS 4

Curriculum topic:  Algebra

Curriculum subtopic:  Simplify/Manipulate Algebraic Expressions/Fractions

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

A polynomial expression is one that contains several algebraic terms, such as

 

3x4 - 5x3 + 2x2 + 3x - 2

 

It is common to write a polynomial expression with terms in decreasing order (x4, x3, x2 etc).

 

When we divide a polynomial expression by a given term, we divide each term in turn.

 

Example

Divide by 2x3:

8x14 - 6x8 + 2x4 - 4x3

 

Answer

We divide each term in turn, remembering to subtract indices and divide coefficients.

  

8x14 - 6x8 + 2x4 - 4x3
2x3 2x3 2x3 2x3

 

This simplifies to

4x11 - 3x5 + x - 2

Divide by x

 

3x4 - 4x3 + 2x2 - 5x

3x4 - 4x3 - 2x2 + x

3x3 - 4x2 + 2x - 5

3x4 - 4x3 - 2x1 + 5x

Divide by x

 

4x4 - 5x3 + 3x2 - 3x

4x4 - 3x3 - 2x2 + x

4x3 - 5x2 + 3x + 3

4x3 - 5x2 + 3x - 3

Divide by 2

 

4x4 - 6x3 + 10x2 - 2x 

8x6 - 2x3 + 5x2 - x

2x4 - 3x3 + 5x2 - x

2x4 - 12x2 + 3x - 1

Divide by 3

 

24x6 - 6x3 + 15x2 - 3x

8x6 - 2x3 + 5x2 - x

8x5 - 2x3 + 5x2 - 1

6x6 - 2x2 + 3x - 1

Divide by 2x

 

4x4 - 6x3 + 10x2 - 2x

8x6 - 2x3 + 5x2 - x

2x4 - 3x3 + 5x2 - x

2x3 - 3x2 + 5x - 1

Divide by 5x

 

40x5 - 35x4 - 10x2 - 20x

8x4 - 7x3 - 2x - 4

8x5 - 7x3 + 5x2 - 4x

10x4 - 7x2 + 5x - 4x

Divide by x2

 

4x5 - 5x4 - 10x3 - 2x2

4x3 - 10x3 - 2x - 2x

4x3 - 5x2 - 10x - 2

3x3 - 5x2 - 2x - 2

Divide by 5x2

 

40x5 - 35x4 - 10x3 - 20x2

8x4 - 7x3 - 2x - 4

8x5 - 7x3 + 5x2 - 4x

8x3 - 7x2 - 2x - 4

Divide by 5x2

 

40x7 + 35x4 - 15x3 - 20x2

8x4 + 7x3 - 2x - 4

8x5 + 7x2 - 3x - 4

8x3 + 7x2 -3x - 4

Divide by 4x3

 

40x7 + 36x6 - 16x4 - 20x3

10x4 + 9x3 - 4x - 5

36x5 + 9x2 - 4x - 5x

10x4 + 9x2 -12x - 5

  • Question 1

Divide by x

 

3x4 - 4x3 + 2x2 - 5x

CORRECT ANSWER
3x3 - 4x2 + 2x - 5
EDDIE SAYS
3x4 - 4x3 + 2x2 - 5x
x x x x
  • Question 2

Divide by x

 

4x4 - 5x3 + 3x2 - 3x

CORRECT ANSWER
4x3 - 5x2 + 3x - 3
EDDIE SAYS
4x4 - 5x3 + 3x2 - 3x
x x x x
  • Question 3

Divide by 2

 

4x4 - 6x3 + 10x2 - 2x 

CORRECT ANSWER
2x4 - 3x3 + 5x2 - x
EDDIE SAYS
4x4 - 6x3 + 10x2 - 2x
2 2 2 2
  • Question 4

Divide by 3

 

24x6 - 6x3 + 15x2 - 3x

CORRECT ANSWER
8x6 - 2x3 + 5x2 - x
EDDIE SAYS
24x6 - 6x3 + 15x2 - 3x
3 3 3 3
  • Question 5

Divide by 2x

 

4x4 - 6x3 + 10x2 - 2x

CORRECT ANSWER
2x3 - 3x2 + 5x - 1
EDDIE SAYS
4x4 - 6x3 + 10x2 - 2x
2x 2x 2x 2x
  • Question 6

Divide by 5x

 

40x5 - 35x4 - 10x2 - 20x

CORRECT ANSWER
8x4 - 7x3 - 2x - 4
EDDIE SAYS
40x5 - 35x4 - 10x2 - 20x
5x 5x 5x 5x
  • Question 7

Divide by x2

 

4x5 - 5x4 - 10x3 - 2x2

CORRECT ANSWER
4x3 - 5x2 - 10x - 2
EDDIE SAYS
4x5 - 5x4 - 10x3 - 2x2
x2 x2 x2 x2
  • Question 8

Divide by 5x2

 

40x5 - 35x4 - 10x3 - 20x2

CORRECT ANSWER
8x3 - 7x2 - 2x - 4
EDDIE SAYS
40x5 - 35x4 - 10x3 - 20x2
5x2 5x2 5x2 5x2
  • Question 9

Divide by 5x2

 

40x7 + 35x4 - 15x3 - 20x2

CORRECT ANSWER
8x5 + 7x2 - 3x - 4
EDDIE SAYS
40x7 + 35x4 - 15x3 - 20x2
5x2 5x2 5x2 5x2
  • Question 10

Divide by 4x3

 

40x7 + 36x6 - 16x4 - 20x3

CORRECT ANSWER
10x4 + 9x3 - 4x - 5
EDDIE SAYS
40x7 + 36x6 - 16x4 - 20x3
4x3 4x3 4x3 4x3
---- OR ----

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