Polynomials & Factor Theorem (AQA GCSE Further Maths)

Topic Questions

1a
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2 marks

straight f left parenthesis x right parenthesis space equals space 3 x cubed space – space 2 x squared space – space 7 x space – space 2

Use the factor theorem to show that left parenthesis 3 x space plus space 1 right parenthesis is a factor of straight f left parenthesis x right parenthesis.

[2]

1b
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3 marks

Factorise straight f left parenthesis x right parenthesis fully.

[3]

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2a
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2 marks

text f end text open parentheses x close parentheses equals 200 x cubed plus 100 x squared minus 18 x minus 9

Use the factor theorem to show that (2x + 1) is a factor of f(x).

[2]

2b
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3 marks

Hence solve  straight f open parentheses x close parentheses equals 0

[3]

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3
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3 marks

straight f open parentheses x close parentheses equals x cubed minus 10 x minus c where c is a positive integer.

left parenthesis x space plus space c right parenthesis is a factor of straight f left parenthesis x right parenthesis.

Use the factor theorem to work out the value of c.

[3]

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4a
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1 mark

Use the factor theorem to show that left parenthesis x space minus space 2 right parenthesis is a factor of x cubed plus space 8 x squared plus 5 x minus 50

[1]

4b
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3 marks

Hence, factorise fully x cubed plus 8 x squared plus 5 x minus 50

[3]

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5a
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2 marks

open parentheses x minus 3 close parentheses is a factor of x cubed minus 8 x squared plus a x plus 42  where a is an integer.

Show that the value of a is 1

[2]

5b
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3 marks

Hence, factorise fully   x cubed minus 8 x squared plus x plus 42

[3]

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