Answer:
The width is: [tex]w(x)=4x^2[/tex]
The length is [tex]l(x)=2x^2+3x+5[/tex]
Step-by-step explanation:
The given rectangle has area given algebraically by the function:
[tex]a(x)=8x^5+12x^3+20x^2[/tex]
The width of the rectangle is the greatest common factor of [tex]8x^5[/tex], [tex]12x^3[/tex] and [tex]20x^2[/tex]
That is the width is: [tex]w(x)=4x^2[/tex]
We now divide the area by the width to obtain the length of the rectangle:
[tex]l(x)=\frac{8x^5+12x^3+20x^2}{4x^2}[/tex]
This simplifies to:
[tex]l(x)=\frac{8x^5}{4x^2}+\frac{12x^3}{4x^2}+\frac{20x^2}{4x^2}[/tex]
[tex]l(x)=2x^2+3x+5[/tex]
Answer:
The width is: [tex]4x^{2}[/tex]
The length is: [tex]2x^{3} +3x+5[/tex]
