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JAMB Mathematics 1978 Question 43

Question 43

Polynomials

If x4 − kx3 + 10x2 + lx − 3 is divisible by (x − 1) and if when it is divided by (x + 2) the remainder is 27, find the constants k and l.

  1. A.k = −7, l = −15
  2. B.k = −15, l = −7
  3. C.k = −21/5, l = −61/5
  4. D.k = −5/3; l = 19/3
  5. E.k = 5/3, l = −19/3
Show the answer and explanation

Answer: A (k = −7, l = −15)

Explanation

f(1) = 0 gives l − k = −8. f(−2) = 27 gives 8k − 2l = −26, i.e. 4k − l = −13. Solving: k = −7 and l = −15.