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WAEC Further Mathematics 2007 Question 24

Question 24

Polynomials

The polynomial g(x) = 2x3 + 3x2 + qx − 1, has the same remainder when divided by (x + 2) and (x − 1). Find the value of constant q.

  1. A.−11
  2. B.−9
  3. C.−3
  4. D.−1
Show the answer and explanation

Answer: C (−3)

Explanation

g(−2) = −16 + 12 − 2q − 1 = −5 − 2q and g(1) = 2 + 3 + q − 1 = 4 + q. Setting them equal: −5 − 2q = 4 + q, so q = −3.