Answer
$(2x-3)(x+1)$
Work Step by Step
The given expression $2x^2-x-3$ has $a=2, b=-1$, and $c=-3$.
Thus, $ac=2(-3)=-6$.
Look for factors of $-6$ whose sum is $b=-1$.
The factors are $-3$ and $2$.
Rewriting $-x$ using the factors found yields $-3x+1x$.
Thus, the given polynomial is equivalent to $2x^2-3x+x-3$
Group the first two terms together and group the last two terms together to obtain:
$(2x^2-3x)+(2x-3)$
Factor out the greateset common factor (GCF) in each group.
$=x(2x-3)+1(2x-3)$
Factor out $(2x-3)$.
$=(2x-3)(x+1)$
