Question

What is the value of `k` for which `(x-1)` is a factor of `(2x^3+9x^2+x+k)`?

Answer 1

`k = -12`

Explanation:

`f(x) = 2x^3 + 9x^2 + x + k`

If `(x-1)` is a factor, then making `x = 1` would make `(x-1)` equal to 0, and everything else in the equation multiply by that 0, resulting to `f(1) = 0`.

`f(1) = 2*1^3 + 9*1^2 + 1 + k = 0`

`f(1) = 2+9+1+k = 0`

`k = -(2+9+1) = - 12`