Question

Find the value of k if x-1 is the factor of x ^ 2 + x + k​

Answer 1

`k = -2`

Explanation:

Recall from the Factor Theorem that if (x - a) is a factor of a polynomial P, then P(a) must equal 0.

Our polynomial is:

`\displaystyle P(x) = x^2 + x + k`

And we know that (x - 1) is a factor.

Therefore, by the Factor Theorem, P(1) must equal 0. Hence solve for k:

`\displaystyle \begin{aligned} P(1) = 0 & = (1)^2 + (1) + k \\ \\ 0 & = 2 + k \\ \\ k & = -2\end{aligned}`

In conclusion, the value of k is -2.