Factors of Polynomials | Cambridge O Level Additional Maths Topic Questions 2025

1a

4 marks

The polynomial $p (x) = 6 x^{3} + a x^{2} + b x + 2$ , where $a$ and $b$ are integers, has a factor of $x - 2$ .
Given that $p (1) = - 2 p (0)$ , find the values of $a$ and $b$ .

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1b

4 marks

Using your values of $a$ and $b$ ,

(i)

find the remainder when

p (x)

is divided by

2 x - 1

(ii)

factorise

p (x)

.

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1a

2 marks

$p (x) = 15 x^{3} + 22 x^{2} - 15 x + 2$

Find the remainder when $p (x)$ is divided by $x + 1$ .

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1b

4 marks

(i)

Show that

x + 2

is a factor of

p (x)

.

[1]

(ii)

Write

p (x)

as a product of linear factors.

[3]

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1a

4 marks

The polynomial $p (x) = a x^{3} - 9 x^{2} + b x - 6$ , where $a$ and $b$ are constants, has a factor of $x - 2$ . The polynomial has a remainder of 66 when divided by $x - 3$ .

Find the value of $a$ and of $b$ .

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1b

2 marks

Using your values of $a$ and $b$ , show that $p (x) = (x - 2) q (x)$ , where $q (x)$ is a quadratic factor to be found.

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1c

2 marks

Hence show that the equation $p (x) = 0$ has only one real solution.

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Factors of Polynomials (Cambridge O Level Additional Maths)

Topic Questions