For what value of k will the polynomial P(x) = x^3 - 2x^2 + kx - 4 have the same remainder when it is divided by x + 3 and by x + 2

Answer 1

By the Remainder Theorem, P(c) is the remainder when P(x) is divided by x - c.

So, we need to find k so that P(-3) = P(-2)

-27 - 18 - 3k - 4 = -8 - 8 - 2k - 4

-49 - 3k = -20 - 2k

So, k = -29

Answer 2

-2 | 1 -2 k -4

-2 8 -2k-16

remainder = -2k -20

-3 | 1 -2 k -4

-3 15 -45 -3k

remainder = -3k-49

set them equal

-2k-20 = -3k -49

k =-29

both remainders = 38