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WMA12/01 Jan 2021, Question 1: The Factor and Remainder Theorems

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 6 marks

The question, in short

Given f(x) = x⁴ + ax³ − 3x² + bx + 5 with constants a and b, use two remainder conditions to form equations and determine a and b.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 2 marks

Using the remainder 4 when f(x) is divided by (x + 1), show that a + b = −1.

  1. 1By the remainder theorem, f(−1) = 4
  2. 2(−1)⁴ + a(−1)³ − 3(−1)² + b(−1) + 5 = 4
  3. 31 − a − 3 − b + 5 = 4
  4. 43 − a − b = 4, so a + b = −1

AnswerShown: f(−1) = 1 − a − 3 − b + 5 = 4, so a + b = −1

Part (b) · 4 marks

Using the remainder −23 when f(x) is divided by (x − 2), find the values of a and b.

  1. 1f(2) = −23: 16 + 8a − 12 + 2b + 5 = −23
  2. 28a + 2b = −32, so 4a + b = −16
  3. 3From (a), b = −1 − a
  4. 44a − 1 − a = −16, so 3a = −15, a = −5
  5. 5b = −1 − (−5) = 4

Answera = −5, b = 4

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Also searched as: WMA12 January 2021 · WMA12/01 · wma12 jan21 · IAS Maths Pure Mathematics 2 January 2021 · question 1.
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