If x\(^4\) - kx\(^3\) + 10x\(^2\) + lx - 3 is divisible by (x -...

JAMB 1978

If x\(^4\) - kx\(^3\) + 10x\(^2\) + 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

A. k = -7, 1 = -15
B. k = -15, 1 = -7
C. k = \(\frac{15}{3}\) , 1 = -7
D. k = \(\frac{7}{3}\) , 1 = -17

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Correct Answer: Option A

Explanation

If k = -7 is put as l = -15, the equation x\(^4\) - kx\(^3\) + 10x\(^2\) + lx - 3 becomes x\(^4\) - (7x\(^3\)) + 10x\(^2\) + (15) -3 = x\(^4\) + 7x\(^3\) + 10x\(^2\) - 15x - 3

This equation is divisible by (x - 1) and (x + 2) with the remainder as 27

k = -7, l = -15

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