For the polynomial

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

For the polynomial t(x)=2x3−5x2−4x+12t(x)=2x^{3}-5x^{2}-4x+12, it is known that x−2x-2 is one of its factors. Which of the following gives the complete factorisation of t(x)t(x)? (a) (x−2)2(2x+3)(x-2)^2(2x+3) (b) (x−2)2(2x−3)(x-2)^2(2x-3) (c) (x−2)(2x+3)(x+2)(x-2)(2x+3)(x+2) (d) (x−2)(x+3)(2x+3)(x-2)(x+3)(2x+3)

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