FUNCTIONS 1B

If f(x) = x⁴ + kx² + 7x + 8 has a remainder of 22 when divided by x+2; find k.

solution

f(x) = x⁴ + kx² + 7x + 8

x + 2 = 0

x = -2

f(x) = (-2)⁴ + k(-2)² + 7(-2) + 8 = 22

16 + 4k + (-14) + 8 = 22

16 + 4k - 6 = 22

16 + 4k = 22 + 6

16 + 4k = 28

4k = 28 - 16

4k = 12

4k = 12

4      4

k = 3

hence k=3

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

If f(x) = x⁴ - kx² + 3x - 8 has a remainder of 30 when divided by x-3; find k.