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2016Q1(a)Factorization of Polynomials (Remainder and Factor Theorems)
NumericalModerate3 marks

Using remainder theorem, find the value of k if on dividing 2x³ + 3x² - kx + 5 by x - 2, leaves a remainder 7.

Topic: Remainder and factor theorem

Previous-year question practice database

Answer

Exam answer

k 13

Explanation
  1. (a) Let f(x) 2x3 3x2 kx 5

Using remainder theorem, f(2) 7 ∴ 2(2)3 3(2)2 k(2) 5 7 ∴ 2(8) 3(4) k(2) 5 7 ∴ 16 12 2k 5 7 ∴ 2k 16 12 5 7 ∴ 2k 26 ∴ k 13

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