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Answer:

Below.

Step-by-step explanation:

We know that area is l x w.

So we know that 4x^4 +24x^2+40x is the area.

The length is 4x.

So let's break this down.

So basically, if it's 4 times the width then.

40x divided by 4x= 10. 24x^2= to 6x because it's dividing by 4x.

Now 4x^4 divided by 4x take away the 4x and you need a common factor so you will get x^3+6x+10 or C.

Answer:

[tex]x^3+6x+10[/tex]

Step-by-step explanation:

The formula for area is:

[tex]A=length*width[/tex]

We can plug in the given lengths into the equation:

[tex]4x^4+24x^2+40x=4x*w[/tex]

Divide both sides by 4x (division property of equality)

[tex]w=\frac{4x^4+24x^2+40x}{4x}[/tex]

[tex]w=\frac{4x^4}{4x}+\frac{24x^2}{4x}+\frac{40x}{4}[/tex]

[tex]w=x^3+6x+10[/tex]

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