A rectangle has an area represented by x^2-4x-12 square feet. If the length is x+2 feet what is the width of the rectangle

Question

Area-x^2-4x-12 

length-x+2

Answer 1

Try factoring the quadratic polynomial.  You should get two binomial factors, each representing a dimension of the rectangle.

Answer 2

Think about how you can factor x^2-4x-12.

given that length=x+2 and area of rectangle = length * width
all you have to do is find the width

there are several way to do this, here is one:
Since one factor of x^2-4x-12 is x+2, x1=-2 is a solution to x62-4x-12=0 so in order to find the other solution, you can use the sum and product properties.

x1*x2= -12 with x1=-2, so x2=6. 

 

Since x2=6, the width of the rectangle is x-6.