Question

Write a simplified polynomial expression in standard form to represent the area of the rectangle below.

A picture of a rectangle is shown with one side labeled as 5 x plus 2 and another side labeled as x minus 4.

A. 5x2 + 18x − 2
B. 5x2 + 13x + 2
C. 5x2 − 18x − 8
D. 5x2 + 13x + 8

Answer 1

(5x+2)(x-4
5x (x)+2(x)+5x (-4)+2 (-4)
5x^2+2x-20x-8
5x^2-18x-8
C. 5x^2-18x-8

Answer 2

The correct option is C.

Explanation:

Given information: One side of the rectangle is (5x+2) and another sides of rectangle is (x-4).

The area of rectangle is

`A=length * width`

Substitute length = (5x+2) and width = (x-4) in the above formula, to find the simplified polynomial expression in standard form to represent the area of the rectangle.

`A=(5x+2)* (x-4)`

Using distributive property,

`A=5x(x-4)+2(x-4)`

`A=5x(x)+5x(-4)+2(x)+2(-4)`

On simplification we get

`A=5x^2-20x+2x-8`

On combining like terms we get

`A=5x^2+(-20x+2x)-8`

`A=5x^2+(-18x)-8`

`A=5x^2-18x-8`

Therefore the correct option is C.