CAIE IGCSE Additional Math 3.2 find polynomial factors

Use this polynomial-factor page to divide by a known factor, find the remaining quadratic factor and write the full product form.

Exam points

Find a quadratic factor Q(x) after a linear factor such as x-2 is known.
Write p(x) as a product of a linear factor and a quadratic factor clearly.
Factorise algebraic expressions by grouping when polynomial-style structure appears.

[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).

$2(2 x+1)\left(4 x^{2}+1\right)$ mark final answer

M1 for $(2 x+1)\left(\frac{\text { their } a^{2}}{2} x^{2} \ldots+2\right)$
or $\left(8 x^{2}+2\right)$ found as quadratic factor

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3.2. Find polynomial factors question 1