The area of a rectangular rug is given by the trinomial r^2 - 8r - 33. What are the possible dimensions of the rug? Use factoring.

Solve for r using factoring:

Solve for r:

r^2 - 8 r - 33 = 0

The left hand side factors into a product with two terms:

(r - 11) (r + 3) = 0

Split into two equations:

r - 11 = 0 or r + 3 = 0

Add 11 to both sides:

r = 11 or r + 3 = 0

Subtract 3 from both sides:

Answer: r = 11 or r = - 3