The cubic polynomial is to be examined for possible linear factors.

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

Problem

The cubic polynomial

q(x)=x^{3}-7x+6

is to be examined for possible linear factors. (i) For each of the polynomials

(x-1)

(x+2)

and

(x-3)

, find the value of

q(x)

at the corresponding value of

x

. (ii) Identify which of the given linear polynomials, if any, are factors of

q(x)

. (iii) For every linear factor identified in part (ii), divide

q(x)

by that factor and write the resulting quadratic factor.