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Please help!

A rectangular tabletop has an area of.......


t^2+2t-99

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

User MohsenJsh
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7.9k points

1 Answer

4 votes

Answer: t-9 and t+11

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

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Step-by-step 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:

  • 1 and -99
  • 3 and -33
  • 9 and -11
  • 11 and -9
  • 33 and -3
  • 99 and -1

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

  • 1 + (-99) = -98
  • 3 + (-33) = -30
  • 9 + (-11) = -2
  • 11 + (-9) = 2 is what we want
  • 33 + (-3) = 30
  • 99 + (-1) = 98

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.

User Raymund
by
8.0k points
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