Question

A rectangle with positive are has length represented by the expression 3x^2+5x-8 and width by 2x^2 +6x write an expression in terms of c for the perimeter and area of the rectangle give your answer in standard polynomial form and show your work

Answer 1

`c=10x^2+22x-16\\A=6x^4+28x^3+14x^2-48x`

Explanation:

Given

Length is
`l=3x^2+5x-8`

Width is
`w=2x^2+6x`

Perimeter of the rectangle is the sum of the sides

`\Rightarrow c=2(3x^2+5x-8+2x^2+6x)\\\Rightarrow c=2(5x^2+11x-8)\\\Rightarrow c=10x^2+22x-16`

Area is given by

`\Rightarrow A=(3x^2+5x-8)(2x^2+6x)\\\Rightarrow A=6x^4+18x^3+10x^3+30x^2-16x^2-48x\\\Rightarrow A=6x^4+28x^3+14x^2-48x`