Answer:
[tex]k = -2[/tex]
Step-by-step 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:
[tex]\displaystyle P(x) = x^2 + x + k[/tex]
And we know that (x - 1) is a factor.
Therefore, by the Factor Theorem, P(1) must equal 0. Hence solve for k:
[tex]\displaystyle \begin{aligned} P(1) = 0 & = (1)^2 + (1) + k \\ \\ 0 & = 2 + k \\ \\ k & = -2\end{aligned}[/tex]
In conclusion, the value of k is -2.
