POLYNOMIALS 1

If f(x) = x⁴ + kx² + 2x -20  has a remainder of 22 when divided by x+2; find k.

solution

f(x) = x⁴ + kx² + 2x - 20 ----------------- (i)

x + 2 = 0

x = -2

_____________________________

Then substitute x = -2 in (i) above

f(x) = (-2)⁴ + k(-2)² + 2(-2) -20 = 22

16 + 4k + (-4) - 20 = 22

16 + 4k -24 = 22    [since -4 – 20 = -24]

4k - 8 = 22       [since 16 – 24 = -8]

4k = 22 + 8

4k = 30

4k = 30

4      4

k = 15/2 = 7.5

hence k=7.5

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

If f(x) = x⁴ - kx² + 6x - 10 has a remainder of 40 when divided by x+3; find k.