What is the value of "k" when P(x)=x^3 - 3x^2 + kx + 2 is divided by x-2 and the remainder is 4?

Answer 1

P(x)=x^3 - 3x^2 + kx + 2
by remainder theroem, put x = 2
(2)^3 – 3(2)^2 + 2k + 2 = 4
8 – 12 + 2 k + 2 = 4
2 k = 4 + 2 = 6
k = 3

Answer 2

by the remainder theorem:
P(2) = 4
but:
P(2) = (2)^3 - 3(2)^2 + k(2) + 2
so:
(2)^3 - 3(2)^2 + k(2) + 2 = 4
8 - 12 + 2k + 2 = 4
2k = 6
k=3

As required

Hope this helps!

Answer 3

at the end of the division, (kx + 2) - k(x-2) = 4, so
2 + 2k = 4
2k = 2
k = 1