Find the value of k such that (x-2) divides evenly into (x^4 - 2x^3 + kx + 8).

Answer 1

Then per remainder theorem, P(2)=0

0= P(2) = 2^4 - 2*2^3 + k(2) + 8

= 16 - 16 + 2k+8

= 2k+8

-8 = 2k

k = -4

check:

x^4 - 2x^3 - 4x + 8 =

x^3(x-2) -4(x-2) =

(x-2) (x^3-4)

of which 2 is a factor

k=-4