Question

If $-4$ is a solution for $x$ in the equation $x^2+kx+8=0$, what is $k$?

Answer 1

$6:$ If $-4$ is a solution, then you know that $(x+4)$ must be one of the factors of the quadratic equation. The other factor is $(x+?)$. You know that the product of $4$ and ? must be equal to $8$; thus , the other factor is $(x+2)$. You know that the sum of $4$ and $2$ must be equal to $k$. Therefore $k=6$

Alternatively, if $-4$ is a solution, then it is possible value for $x$. Plug it into the equation for $x$ and solve for $k$:

$x^2+kx+8=0$

$16-4k+8=0$

$24=4k$

$k=6$