Question

The rectangle below has an area of y^4+11y^2+30 square meters and a length of y^2+5 meters. What represents the width of the rectangle?

Answer 1

`y^2+6\ m`

Explanation:

First factor the expression
`y^4+11y^2+30:`

`y^4+11y^2+30=y^4+5y^2+6y^2+30=y^2(y^2+5)+6(y^2+5)=(y^2+5)(y^2+6).`

Use the formula

`A_{\text{rectangle}}=\text{width}\cdot \text{length}`

for finding the area of the rectangle.

If the length of the rectangle is
`y^2+5` meters, then its width is

`\text{width}=\frac{A_{\text{rectangle}}}{\text{length}}=(y^4+11y^2+30)/(y^2+5)=((y^2+5)(y^2+6))/(y^2+5)=y^2+6\ m.`