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JAMB Mathematics 1980 Question 42

Question 42

Polynomials

The expression x3 − 4x2 + cx + d is such that x + 1 is its factor, and its value is 1 when x is −2. Find c and d.

  1. A.c = 4 and d = −9
  2. B.c = −4 and d = 9
  3. C.c = −20 and d = −15
  4. D.c = 20 and d = −15
  5. E.c = −20 and d = 15.
Show the answer and explanation

Answer: C (c = −20 and d = −15)

Explanation

f(−1) = −1 − 4 − c + d = 0 gives d − c = 5. f(−2) = −8 − 16 − 2c + d = 1 gives d − 2c = 25. Subtracting: c = −20, so d = −15.