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: Option C
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