Question

find the value of k so that the remainder is 5. X^2+8X+17 divided by X+K

Answer 1

X^2+8X+17

Answer 2

f(-k) = k^2 - 8k + 17
you want f(-k) = 5

k^2 - 8k + 12 = 0
(k-6)(k-2) = 0

so, for k = 2 or 6,

(x^2 + 8x + 17)/(x-2) = x+6 R 5
(x^2 + 8x + 17)/(x-6) = x+2 R 5

Answer 3

oops. we divide by x+k, so k = -2 or -6