Answer
$(x-3)(7x-16)$
Work Step by Step
The given expression is $7(x^2-6x+9)+5(x-3)$.
First, factor $x^2-6x+9$
Rewrite $-6x$ as $-3x-3x$.
$=x^2-3x-3x+9$
Group the first two terms together and group the last two terms together.
$=(x^2-3x)+(-3x+9)$
Factor out the GCF in each group.
$=x(x-3)-3(x-3)$
Factor out $(x-3)$.
$=(x-3)(x-3)$
Next, substitute back the above factored form into the given expression.
$7(x^2-6x+9)+5(x-3)=7(x-3)(x-3)+5(x-3)$
Factor out $(x-3)$.
$=(x-3)[7(x-3)+5]$
Use distributive property to simplify.
$=(x-3)(7x-21+5)$
$=(x-3)(7x-16)$
Hence, the complete factor form is $(x-3)(7x-16)$.
