Answer
The polynomial changes to $x^{2}-\frac{3}{2}x-\frac{77}{2}$.
Work Step by Step
When the longer base is extended by 1 foot, $b_{2}$ becomes
$b_{2}=(x+10)\,ft+ 1\,ft=(x+11)\,ft$
The polynomial that represents the area is then
$A=\frac{1}{2}h(b_{1}+b_{2})=\frac{1}{2}(x-7)[x+(x+11)]$
Combining like terms, we have $A=\frac{1}{2}(x-7)(2x+11)$
Now, use FOIL(First Outer Inner Last) method to get
$A=\frac{1}{2}[2x^{2}+11x+(-14x)+(-77)]$
Combining like terms, we have
$A=\frac{1}{2}(2x^{2}-3x-77)$
Using distributive property, we obtain
$A=x^{2}-\frac{3}{2}x-\frac{77}{2}$.
