Wednesday's Notes ...

Yesterday, we reviewed how to find the greatest common factor (gcf). We added to this concept how to factor it out of the polynomial.

Example: Factor 9a³ + 12a² - 15a

1. Look at each number and identify the largest number that can go into each evenly. Here, 3 goes into 9, 12, and -15 evenly.
2. Look at each variable and identify how many each term has in common with the others. The students were told to find the smallest exponent because that term limits how many the others can have in common. Here, each term has one a-variable. While the first and second terms have more a-variables, the last term only has one so it limits the common factor.
3. Write the GCF and then start parenthesis after that: 3a ( ______ )
4. To find what polynomial goes inside the parenthesis, determine term by term either "what is left when we divide by the gcf" or "what multiplies with the gcf to make the term". Here, 3a * 3a² makes the first term of 9a³. 3a * 4a makes 12a². And, 3a * -5 makes -15a. So, the final answer after factoring out the gcf is 3a (3a² + 4a - 5).
5. We can check every factoring problem by multiplying the factors back together. Their product should be the original polynomial. Remember, add exponents when multiplying bases. Here: 3a * 3a² + 3a * 4a + 3a * -5 = 9a³ + 12a² - 15a.

Homework: Page 79: #13 - 21 and Page 80: #10 - 18

There will be a quiz on Thursday, October 29 on factoring and solving by factoring (for the next week).

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