Question

Write a polynomial in standard form that represents the area of the shaded region.

Answer 1

Answer:

$A=p^2-2p-3$

Step-by-step explanation:

The area for a triangle is given by:

$\displaystyle A=\frac{1}{2}bh$

The base is p + 1 and the height is 2p - 6. Therefore:

$\displaystyle A=\frac{1}{2}(p+1)(2p-6)$

Simplify the second term:

$\displaystyle A=(p+1)(\frac{1}{2})(2p-6)=(p+1)(p-3)$

Distribute:

$A=p(p-3)+1(p-3)$

Distribute:

$A=p^2-3p+p-3$

Combine like terms:

$A=p^2-2p-3$