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 2 x minus 4 and another side labeled as x plus 5

Answer 1

A = w × l
A = (2x - 4) (x + 5)
Next Step Foil
2x² + 10x - 4x -20
2x² + 6x - 20

Answer 2

A simplified polynomial expression in standard form to represent the area of the rectangle below is:

`2x^2+6x-20`

Explanation:

We are given a rectangular figure such that the length of one side is given as: 2x-4

while the other side is labelled as: x+4.

Let us assume that the length of rectangle(l)= 2x-4

and width or breadth of rectangle(b)=x+5

We know that the area of rectangle(A) is given as:

A=l×b.

A=(2x-4)×(x+5)

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

A=2x^2+10x-4x-20

A=2x^2+6x-20.

Hence, the polynomial expression for the area of rectangle is a polynomial of degree 2 and is given by:

`2x^2+6x-20`