Question

How do you find the value of k so that the remainder is zero given `(x^3+4x^2-kx+1)div(x+1)`?

Answer 1

`k = -4`

Explanation:

`f(x) = x^3+4x^2-kx+1`

By the remainder theorem, the remainder when dividing a polynomial `f(x)` by `(x-a)` is `f(a)`

In our case, we have `a=-1` and we need:

`0 = f(-1) = (-1)^3+4(-1)^2-k(-1)+1`

`color(white)(0 = f(-1)) = -1+4+k+1`

`color(white)(0 = f(-1)) = k+4`

Hence `k = -4`