The area of a rectangular rug is given by the trinomial r^2-4r-21. What are the possible dimensions of the rug?

There are two possible values for r (area):  r =-7 or r=3

Step-by-step explanation:

Given the rectangular rug area is:

We have to convert the above equation into factored form.

So two numbers whose product is -21r² and sum is -4r

<=>  

=

= r (r -7) + 3(r -7)

= (r-7)(r+3)

We set     = 0

<=> (r-7)(r+3) = 0

<=> (r-7) = 0 or (r+3)  = 0

<=> r =-7 or r=3

So, there are two possible values for r (area):  r =-7 or r=3