Question

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

Answer 1

1/2•(2p-6)(p+1)
1/2•(2p^2+2p-6p-6)
1/2•(2p^2-4p-6)
p^2-2p-3

Answer 2

The polynomial in standard form that represents the area of the shaded region is $=\rm p^2-2p-3$

Given:  A Right angled triangle, where

                  Perpendicular = 2p-6

                  Base                = p+1

Now to find the equation of polynomial ,we will be using Area of right angle triangle.          

What is The Area of Triangle?

To find the area of right angled triangle we will use its formula

Area of right angled triangle,  

= $\rm \dfrac{1}{2}\times length \times breadth$ we usually represent the height or length of the right-angled triangle as perpendicular.

Now according to the formula of right angled triangle we will solve further we get.

$=\rm \dfrac{1}{2} \times (2p-6)(p+1)\\=\rm \dfrac{1}{2}\times (2p^2+2p-6p-6)\\=\rm \dfrac{1}{2} \times (2p^2-4p-6)\\=\rm p^2-2p-3$

Therefore, the area of the shaded region is in polynomial form       i.e. $=\rm p^2-2p-3$

Learn more about Polynomial here : https://brainly.com/question/1256199