2006
Mathematics
JAMB
Find the value of k if the expression kx3 + x2 - 5x - 2 leaves a remainder 2 when it is divided by 2x + 1
A.
10
B.
8
C.
-10
D.
-8
Correct Answer: -10
Explanation
F(x) = Q x D + R Kx3 + x2 - 5x – 2 = Q(2x+1)+R If 2x+1 = 0 implies x = -1/2 ∴k(-1/2)3 + (-1/2)2 -5(-1/2) -2 = Q(2(-1/2) + 1) +2 K(-1/8) + 1/4 + 5/2 - 2 = Q(-1+1)+2 -k/8 + 1/4 + 5/2 - 2 = 0+2 (-k+2+20-16) / 8 = 2 (-k+6) / 8 = 2 -k+6 = 2*8 -k+6 = 16 -k = 16-6 -k = 10 ∴k = -10
F(x) = Q x D + R Kx3 + x2 - 5x – 2 = Q(2x+1)+R If 2x+1 = 0 implies x = -1/2 ∴k(-1/2)3 + (-1/2)2 -5(-1/2) -2 = Q(2(-1/2) + 1) +2 K(-1/8) + 1/4 + 5/2 - 2 = Q(-1+1)+2 -k/8 + 1/4 + 5/2 - 2 = 0+2 (-k+2+20-16) / 8 = 2 (-k+6) / 8 = 2 -k+6 = 2*8 -k+6 = 16 -k = 16-6 -k = 10 ∴k = -10THIS WEEK's
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