FUNCTIONS 7

If f(x) = x⁴ + kx² + 3x + 8 has a remainder of 22 when divided by x+2; find k.

solution

f(x) = x⁴ + kx² + 3x + 8

x + 2 = 0

x = -2

f(x) = (-2)⁴ + k(-2)² + 3(-2) + 8 = 22

16 + 4k + (-6) + 8 = 22

16 + 4k + 2 = 22

4k + 18 = 22

4k = 22 - 18

4k = 4

4k = 4

4      4

k = 1

hence k=1

TRY THIS......................

If f(x) = x⁴ - kx² + 3x - 8 has a remainder of 40 when divided by x+3; find k.