The area of a rectangle is (x4 + 4x3 + 3x2 – 4x – 4), and the length of the rectangle is (x3 + 5x2 + 8x + 4). If area = length × width, what is the width of the rectangle

The width of the rectangle, for which area and length provided in polynomial equation form is,[tex](x^43x^3+8x^2+4x)[/tex]What is the area of a rectangle?Area of a rectangle is the product of the length of the rectangle and the width of the rectangle. It can be given as,[tex]A=a\times b[/tex]Here, (a)is the length of rectangle and (b) is the width of the rectangleThe area of the given rectangle is,[tex]A=(x^4 +4x^3 +3x^2 - 4x - 4),[/tex]The length of the given rectangle is,[tex]L=x^3+ 5x^2 +8x+ 4).[/tex]As, the area of a rectangle is the product of the length and the width of the rectangle. Let suppose the width of the rectangle is f(x). Therefore,[tex](x^4 +4x^3 +3x^2 - 4x - 4)=(x^3+ 5x^2 +8x+ 4)\times f(x)[/tex]Solve it further as,[tex]f(x)=(x^4 +4x^3 +3x^2 - 4x - 4)-(x^3+ 5x^2 +8x+ 4) \\f(x)=(x^4 +4x^3 +3x^2 - 4x - 4-x^3+ 5x^2 +8x+ 4[/tex]Separate the like terms with same power of variable as,[tex]f(x)=x^4 +4x^3-x^3 +3x^2 + 5x^2- 4x +8x- 4 + 4\\f(x)=x^43x^3+8x^2+4x[/tex]Hence, the width of the rectangle, for which area and length provided in polynomial equation form is,[tex](x^43x^3+8x^2+4x)[/tex]Learn more about the area of rectangle here;