FUNCTIONS B1

 

If f(x) = x⁴ + kx² + 6x + 7 has a remainder of 91 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 = 91

 

16 + 4k + (-12) + 7 = 91

 

16 + 4k - 12 + 7 = 91

 

16 + 4k - 5 = 91

 

4k + 16 - 5 = 91

 

4k + 11= 91

 

4k = 91 - 11

 

4k = 80

 

4k = 80

4      4

 

k = 20

 

hence k = 20

 

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

 

 

If f(x) = x⁴ - hx² + 2x - 13 has a remainder of 16 when divided by x-3; find h.