Question

The length of a rectangle is represented by the polynomial 2x^3-5x^2+8 and the width is represented by the polynomial x+3. Complete the following statements about the polynomial that represents the area of the rectangle

Answer 1

The area of rectangle is
`2x^4 + x^3 -15x^2 +8x +24`.

Explanation:

Given that,

Length of rectangle =
`2x^3-5x^2+8`

Width of rectangle =
`x + 3`

Area of rectangle = A = ?

Area of a rectangle is calculated by multiplying length with width

A = l * w

In our case

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

`w = x + 3`

`A = l * w`

=>
`(2x^3-5x^2+8)*(x+3)`

=>
`x*(2x^3-5x^2+8) +3(2x^3-5x^2+8)`

=>
`(2x^4-5x^3+8x) +(6x^3-15x^2+24)`

=>
`(2x^4) + (-5x^3+6x^3) + (-15x^2)  +(8x) +(24)`

=>
`(2x^4) + (x^3) + (-15x^2)  +(8x) +(24)`

=>
`2x^4 + x^3 -15x^2 +8x +24`

Therefore, the area of rectangle is
`2x^4 + x^3 -15x^2 +8x +24`.