The area of a rectangular outdoor stage has been extended on one side. The entire new area in square meters can be written as 216plus12x. Factor the expression to find the dimensions of the extended stage.
We want to factor the expression $216+12x$ to find the dimensions of the extended stage.
First, let's factor out the greatest common factor of $216$ and $12$, which is $12$. We can rewrite the expression as: $$12(18+x)$$
Now, we have the expression $18+x$. In order to factor this further, we need to find two numbers whose product is $18$ and whose sum is $x$. The numbers $2$ and $9$ satisfy these conditions.
Therefore, we can factor the expression completely as: $$12(2+9)(9)$$
The dimensions of the extended stage are $2+9$ meters by $9$ meters, or $11$ meters by $9$ meters.