Please help! A rectangular tabletop has an area of.


What are the possible dimensions of the tabletop? Use factoring.

The order doesn't matter, so you could say "t+11 and t-9" to mean the same thing.

Explanation:

Think of two numbers that multiply to -99, but also add to 2. In other words, find two factors of -99 which add to 2. We'll use trial and error.

Here are all the ways to multiply to -99 using integers only:

Add up each factor pair to see which sum is equal to 2.

We can see that 11 and -9 are the two numbers we're after, so therefore, t^2+2t-99 factors to (t-9)(t+11). The order doesn't matter with the factor multiplication.

As a more efficient alternative method, you can use the quadratic formula to solve t^2+2t-99 = 0 to end up with t = 9 and t = -11. That would lead to the  two equations t-9 = 0 and t+11 = 0. Applying the zero product property then gets us (t-9)(t+11) = 0.

To help show that (t-9)(t+11) becomes t^2+2t-99, you can use the FOIL rule to expand that factorization out. This is one way to verify the answer.