Answer
$(x+5)(x+3)$.
Work Step by Step
The given expression is
$x^2+8x+15$
The trinomial is of the form $ax^2+bx+c$.
By comparing the given expression with standard form we have.
$a=1,b=8$ and $c=15$.
Multiply $a$ and $c$
$a\cdot c = 1\cdot 15$
$a\cdot c = 15$
Now find the factors of $a\cdot c$ whose sum is equal to $b$.
The factors are $5+3 =b = 8$.
Rewrite the middle term $8x$ as $5x+3x$.
$x^2+5x+3x+15$
Group terms.
$(x^2+5x)+(3x+15)$
Factor from each group.
$x(x+5)+3(x+5)$
Factor out $(x+5)$.
$(x+5)(x+3)$.
Hence, the factors are
$x^2+8x+15 = (x+5)(x+3)$.
