Answer the following questions about the factorisation of cubic polynomials.

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Answer the following questions about the factorisation of cubic polynomials. (i) State the Factor Theorem. (ii) Let

q(x)=x^{3}+5x^{2}+8x+4

. Explain why the value

x=-2

being a zero of

q(x)

guarantees that

(x+2)

divides

q(x)

. (iii) Verify that

(x+2)

is indeed a factor of

q(x)

and write

q(x)

in completely factorised form.