Mathematics

Find the value of k if the expression kx3 + x2 – 5x – 2…

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