POLYNOMIALS 2

If f(x) = x⁴ + kx² + 3x + 7 has a remainder of 22 when divided by x+2; find k.

solution

f(x) = x⁴ + kx² + 3x + 7

x + 2 = 0

x = -2

f(x) = (-2)⁴ + k(-2)² + 3(-2) + 7 = 22

16 + 4k + (-6) + 7 = 22

16 + 4k + 1 = 22

4k + 17 = 22

4k = 22 - 17

4k = 5

4k = 5

4      4

k = 5/4

hence k=5/4

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

If f(x) = x⁴ - kx² + 3x - 8 has a remainder of 20 when divided by x-3; find k.