Answer
not factorable with integer coefficients
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the quadratic expression $ax^2+bx+c,$ find two numbers whose product is $ac$ and whose sum is $b$. Use these $2$ numbers to decompose the middle term of the quadratic expression and then use factoring by grouping.
$\bf{\text{Solution Details:}}$
In the given expression, $
40x^2+xy+6y^2
,$ the value of $ac$ is $
40(6)=240
$ and the value of $b$ is $
1
.$
The possible pairs of integers whose product is $ac$ are
\begin{array}{l}\require{cancel}
\{1,240\}, \{2,120\}, \{3,80\}, \{4,60\}, \{5,48\}, \{6,40\}, \{8,30\}, \{10,24\}, \{12,20\}, \{15,16\},
\{-1,-240\}, \{-2,-120\}, \{-3,-80\}, \{-4,-60\}, \{-5,-48\}, \{-6,-40\}, \{-8,-30\}, \{-10,-24\}, \{-12,-20\}, \{-15,-16\}
.\end{array}
None of these pairs give a sum of $b$. Hence, the given expression is $\text{
not factorable with integer coefficients
.}$