Back It All Out
On the last page, we looked at multiplying expressions. Now, we will take the answers from the last page and factor them. Factoring involves finding the greatest common factor, the biggest number that fits into the numbers in the expressions. Don’t forget though, since we are dealing with coefficients, to subtract from the letters too.
Let’s look at the first answer from the last page: 5x² + 5xy -20x . The number 5 and x are the common factors so we will place 5x outside of the parenthesis and leave the rest inside.
5x(x + y – 4)
As always, check your work! Mistakes can happen on the simplest of problems. To check, work just like we did on the previous page. Multiply each term by the terms in the parenthesis. If it matches up with the original, you are good to go!
Reversal of “FOILtune”
Okay, that was a terrible pun, but we are sticking with it. Let’s reverse the second example that Liesel did on her chalkboard: x² – 4.
First, we will break down x². We know we can get that by multiplying x by itself, x(x). We are halfway done already.
Next, determine the factors of 4. They are 1, 2, and 4. Which of these numbers will equal -4 if multiplied together *and* has the middle term cancel out? Here is where you may need to test your factors to see which one works out to the desired answer.
Think it through! You knew that the equation needed opposing signs because the last number was negative. If the equation had been (x + 2)(x + 2) or (x – 2)(x – 2), then you would have had + 4. Although factors 1 and 4 can give us the result of -4, they wouldn’t cancel out no matter what sign you used. Only the factor 2 fit both criteria.
Another Equation FOILed by Factoring
The puns are so strong with this page. We just can’t help ourselves. Ok, moving on. Since FOIL factoring can be a bit confusing, let’s look at a couple more examples.
Get in the habit of working your answer to make sure it calculates back to the original problem.