Answer
The number to add is $49$.
The factored form is $(p+7)^2$.
Work Step by Step
The given expression is $p^2+14p$.
This is in the form of $p^2+bp$ where $b=14$.
To find what number must be added to compelte the square, use the formula $\left(\frac{1}{2}b\right)^2$.
$\Rightarrow \left(\frac{1}{2}b\right)^2=\left(\frac{1}{2}\cdot 14\right)^2=7^2=49$
Add $49$ to the given expression.
$=p^2+14p+49$
$=p^2+2\cdot 7 \cdot p+7^2$
Use the special formula $a^2+2ab+b^2=(a+b)^2$ where $a=p$ and $b=7$.
$=(p+7)^2$
Hence, the factored form is $(p+7)^2$.
