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

Answer:

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

Step-by-step explanation:

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

Breadth of Rectangle = $x+3$

Formula of area of rectangle = $Length \times Breadth$

                                               = $(2x^3-5x^2+8)\times (x+3)$

                                               = $x(2x^3-5x^2+8)+3(2x^3-5x^2+8)$

                                               = $2x^4-5x^3+8x+6x^3-15x^2+24$

                                               = $2x^4+x^3-15x^2+8x+24$

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

Answer 2

X+3(2x^3-5x^2+8)
= $6 x^{3} -15x^{2}+ x+24$