Let be any real number and let .

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

Problem

Let tt be any real number and let p(x)=4x3−3x2+2x−5p(x)=4x^{3}-3x^{2}+2x-5. (i) Find the remainder obtained when p(x)p(x) is divided by x−(2t+1)x-(2t+1), expressing your answer in terms of tt. (ii) Using your result from part (i), determine the remainder when t=2t=2.

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