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:The area of rectangle is [tex]2x^4 + x^3 -15x^2 +8x +24[/tex].Step-by-step explanation:Given that,Length of rectangle = [tex]2x^3-5x^2+8[/tex]Width of rectangle = [tex]x + 3[/tex] Area of rectangle = A = ?Area of a rectangle is calculated by multiplying length with widthA = l * wIn our case[tex]l = 2x^3-5x^2+8[/tex][tex]w = x + 3[/tex][tex]A = l * w[/tex]=> [tex](2x^3-5x^2+8)*(x+3)[/tex]=> [tex]x*(2x^3-5x^2+8) +3(2x^3-5x^2+8)[/tex]=> [tex](2x^4-5x^3+8x) +(6x^3-15x^2+24)[/tex]=> [tex](2x^4) + (-5x^3+6x^3) + (-15x^2)  +(8x) +(24)[/tex]=> [tex](2x^4) + (x^3) + (-15x^2)  +(8x) +(24)[/tex]=> [tex]2x^4 + x^3 -15x^2 +8x +24[/tex]Therefore, the area of rectangle is [tex]2x^4 + x^3 -15x^2 +8x +24[/tex].