Answer
$(x+5)(3x+11)$
Work Step by Step
The given expression is $3(x^2+10x+25)-4(x+5)$.
First, factor $x^2+10x+25$
Rewrite $10x$ as $5x+5x$.
$=x^2+5x+5x+25$
Group the first two terms together and group the last two terms together.
$=(x^2+5x)+(5x+25)$
Factor out the GCF in each group.
$=x(x+5)+5(x+5)$
Factor out $(x+5)$.
$=(x+5)(x+5)$
Substitute back into the given expression.
$3(x^2+10x+25)-4(x+5)=3(x+5)(x+5)-4(x+5)$
Factor out $(x+5)$.
$=(x+5)[3(x+5)-4]$
Use distributive property.
$=(x+5)(3x+15-4)$
$=(x+5)(3x+11)$
Hence, the completely factored form of the given expression is $(x+5)(3x+11)$.
