IGCSE Additional Math 3.2. Find polynomial factors Topic Practice

CAIE IGCSE Additional Math 3.2. Find polynomial factors question practice helps you revise this syllabus point with the course map in view. Use this page to focus on one topic, check the style of questions available, and connect each attempt back to the knowledge area it is testing.

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3.2.1—Find polynomial factors

[Maximum number: 2]

The polynomial $\mathrm{p}(x)=6 x^{3}+a x^{2}+b x+2$ , where a and b are integers, has a factor of x-2.

Using your values of a and b,

factorise p(x).

[Maximum number: 2]

DO NOT USE A CALCULATOR IN THIS QUESTION.

The polynomial p is such that $\mathrm{p}(x)=6 x^{3}-35 x^{2}+34 x+45$ .

Hence write the expression p(x)-5 as a product of linear factors.

[Maximum number: 2]

The diagram shows the graph of y=h(x) where $\mathrm{h}(x)=(x+a)^{2}(b+c x)$ and a, b and care integers. The curve meets the x -axis at the points (-2,0) and (1.5,0) and the y -axis at the point (0,12).

Find the values of a , b and c .

[Maximum number: 2]

The polynomial p is given by $\mathrm{p}(x)=a^{2} x^{3}+2 a x^{2}+a x+2$ , where a is a positive integer. It is given that 2 x+1 is a factor of p(x).

Hence factorise p(x).

[Maximum number: 3]

The polynomial p is such that $\quad \mathrm{p}(x)=3 x^{3}-7 x^{2}+a x+b$ , where a and b are integers.
It is given that $\mathrm{p}^{\prime}(-1)=21$ and that x-2 is a factor of p(x).

Hence write p(x) as a product of linear factors with integer coefficients.

[Maximum number: 3]

The polynomial p is such that $\mathrm{p}(x)=6 x^{3}+x^{2}-12 x+5$ ．

（ii）Hence write p(x) as a product of linear factors．

[Maximum number: 2]

$7 \mathrm{p}(x)=a x^{3}+3 x^{2}+b x-12$ has a factor of 2 x+1. When p(x) is divided by x-3 the remainder is 105.

Using your values of a and b, write p(x) as a product of 2 x+1 and a quadratic factor.

[Maximum number: 6]

$\mathrm{p}(x)=6 x^{3}+a x^{2}+12 x+b$ , where a and b are integers.
p(x) has a remainder of 11 when divided by x-3 and a remainder of -21 when divided by x+1.

Given that p(x)=(x-2) Q(x), find Q(x), a quadratic factor with numerical coefficients.

[Maximum number: 1]

Write 6 x y+3 y+4 x+2 in the form ( a x+b)(c y+d), where a, b, c and d are positive integers.

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Question 2(b)(ii)

Question 2(b)

Question 3(a)

Question 4(b)

Question 5(b)

Question 4(b)(ii)

Question 7(b)

Question 5(a)

Question 9(a)(i)