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TMUA 2017 · Paper 1 · Question 4 of 20

TMUA 2017 Paper 1 Question 4

Algebra and functions — Remainder theorem. Try it first; the answer and a full worked solution are below.

TMUA 2017 · Paper 1Algebra and functionsRemainder theorem5 options
When (3x2 + 8x − 3) is multiplied by (px − 1) and the resulting product is divided by (x + 1), the remainder is 24.

What is the value of p?

  1. A−4
  2. B2
  3. C4
  4. D87
  5. E114
Show the answer and worked solution
answer · B
  1. A−4
  2. B2
  3. C4
  4. D87
  5. E114
There is no need to expand: the remainder on division by (x+1) is the value of the product at x = −1. Here 3(−1)2 + 8(−1) − 3 = −8 and p(−1) − 1 = −p − 1, so the remainder is (−8)(−p−1) = 8p + 8. Setting 8p + 8 = 24 gives p = 2.