Answer
not factorable with integer coefficients
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
9x^2+13xy-3y^2
,$ find two numbers whose product is $ac$ and whose sum is $b$ in the quadratic expression $ax^2+bx+c.$ Use these $2$ numbers to decompose the middle term of the given quadratic expression and then use factoring by grouping.
$\bf{\text{Solution Details:}}$
To factor the trinomial expression above, note that the value of $ac$ is $
9(-3)=-27
$ and the value of $b$ is $
13
.$
The possible pairs of integers whose product is $ac$ are
\begin{array}{l}\require{cancel}
\{1,-27\}, \{3,-9\},
\\
\{-1,27\}, \{-3,9\}
.\end{array}
Among these pairs, there is none that gives a sum of $b$. Hence, the given expression is $\text{
not factorable with integer coefficients
.}$
