Answer
$v^2+12v+20=(v+10)(v+2)$
Work Step by Step
We are trying to fill in the blank in the equation $v^2+12v+20=(v+10)(v+\square).$ In order to do so, we will factor the trinomial on the left side of the equation, to determine the second factor.
To factor a trinomial in the form $x^2+bx+c$, we must find two numbers whose product is $c$ and whose sum is $b$. We then insert these two numbers into the blanks of the factors $(x+\_)(x+\_)$.
In the case of $v^2+12v+20$, we are looking for two numbers whose product is $20$ and whose sum is $12$. The numbers $10$ and $2$ meet these criteria, because $$10\times(2)=20\;\text{and}\;10+(2)=12$$When we insert these numbers into the blanks, we arrive at the factors $(v+10)(v+2)$.
