Question

Factoring quadratics introThe rectangle below has an area of x2 + 11x + 28 square meters and a length of x + 7 meters.What expression represents the width of the rectangle?

Answer 1

Answer: The width is x + 4

Step-by-step explanation

• The area (,A,) is:

`A=x^2+11x+28`

• The length (,l,) is:

`l=x+7`

The formula for the area of a rectangle is:

`A=l* w`

where w represents the width.

Then, to get the width we have to isolate it in the formula:

`w=(A)/(l)`

Replacing the expressions given:

`w=(x^2+11x+28)/(x+7)`

To simplify this expression we can factor the numerator by finding two numbers that when added equal 11, and when multiplied equal 28. For example, 4 and 7:

`4+7=11`
`4*7=28`

Then, the expression is:

`w=(\left(x+4\right)\left(x+7\right))/(x+7)`

Simplifying:

`w=(x+4)((x+7))/(x+7)`
`w=(x+4)*1`

Then the width is x + 4.