FUNCTIONS 3

If f(x) = x⁴ - kx² - 6x + 7 has a remainder of 22 when divided by x+2; find k.

solution

f(x) = x⁴ - kx² - 6x + 7

x + 2 = 0

x = -2

f(x) = (-2)⁴ - k(-2)² - 6(-2) + 7 = 22

16 - 4k + 12 + 7 = 22

16 - 4k + 19 = 22

16 + 19 = 22 + 4k

16 + 19 - 22=4k

35 - 22=4k

13 = 4k

k = ¹³/4    after dividing by 4 both sides.

hence k=¹³/4

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

If f(x) = x⁴ - kx² - 5x - 31 has a remainder of 18 when divided by x-2; find k.