Question

Find k such that x+3 is a factor of s(x)=x^3 +kx^2 +kx-15???

I have no idea how to do this problem at all, but I do know that k=7. Please help I appreciate it SOOO much!!!

Answer 1

k = 7

Explanation:

If x + 3 is a factor of s(x), then from the remainder theorem,

              s(-3) = 0

this implies that,
`(-3)^3` + k`(-3)^2` +k(-3) - 15 = 0

-27 + 9k -3k - 15 = 0

6k - 42 = 0

6k = 42

dividing through by 6 gives,

k = `42/6`

`therefore`k = 7