Question

can you please list all of the possible integers that could replace K in the expression $6 {x }^{2} + kx - 8$so that the expression can be factored using integers.

Answer 1

SOLUTION

We are given the expression

$\begin{gathered} 6x^2+kx-8 \\ to\text{ list all the possible integers that could replace k so that the expression} \\ \text{can be factorized } \end{gathered}$

To do this, we say

$\begin{gathered} 6x^2\text{ }\times\text{ }-8=-48x^2 \\ \text{now we list all the possible factors of }-48x^2\text{ and sum them to get k} \\ -48+\text{ 1 = -4}7 \\ -24\text{ + 2 = -22} \\ 48\text{ + (-1) = 47} \\ 24\text{ + (-2) = 22} \\ -16\text{ + 3 = -13} \\ 16\text{ + (-3) = 13} \\ -12\text{ + 4 = -8} \\ 12\text{ + (-4) = }8 \\ -\text{ 8 + 6 = -2} \\ 8+\text{ (-6) = 2} \end{gathered}$

Therefore the possible values of k are -47, 47, -22, 22, -13, 13, -8, 8, -2 and 2