Question

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

Answer 1

`A=p^2-2p-3`

Explanation:

The area for a triangle is given by:

`\displaystyle A=(1)/(2)bh`

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

`\displaystyle A=(1)/(2)(p+1)(2p-6)`

Simplify the second term:

`\displaystyle A=(p+1)((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`