Question

How do you determine the value of k if the remainder is 3 given `(x^3+4x^2-x+k)div(x-1)`?

Answer 1

`k = -1`.

Explanation:

the remainder theorem states that if a polynomial `p(x)` is divided by `x - a`, then the remainder is given by `p(a)`.

Here, `a = 1` and the remainder is `3`.

So:

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

`1 + 4 - 1 + k = 3`

`k = -1`

Hopefully this helps!