The rectangle below has a length of 3x2+7x-5and a width of - x2-4x+2. Find the perimeter of the rectangle and explain how you arrived at your solution.

P = 4x² + 6x - 6

Step-by-step explanation:

We will use the formula for perimeter in terms of side lengths, then fill in the values given for the side lengths and simplify the result.

The perimeter (P) of a rectangle is given by the formula ...

P = 2 (L + W)

where L and W represent the length and width. Filling in your given information, we have ...

P = 2 ((3x² + 7x - 5) + (-x² - 4x + 2)) j

Collecting terms inside parentheses gives ...

P = 2 ((3-1) x² + (7-4) x + (-5+2)) = 2 (2x² + 3x - 3)

Using the distributive property gives ...

P = 4x² + 6x - 6