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

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

Answer 2

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

Explanation:

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

Breadth of Rectangle =
`x+3`

Formula of area of rectangle =
`Length * Breadth`

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

Hence the polynomial that represents the area of the rectangle is
`2x^4+x^3-15x^2+8x+24`.