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fenix001 [56]
3 years ago
12

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

Mathematics
1 answer:
Ne4ueva [31]3 years ago
4 0

Answer:

k = -2

Step-by-step explanation:

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

Our polynomial is:

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

And we know that (<em>x</em> - 1) is a factor.

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

<em />\displaystyle \begin{aligned} P(1) = 0 & = (1)^2 + (1) + k \\ \\ 0 & = 2 + k \\ \\ k & = -2\end{aligned}

In conclusion, the value of <em>k</em> is -2.

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