1. Bell Ringer 2-26-18 1. What is a factor tree?
2. What are the terms at the bottom of a
factor tree called?
3. What is GCF?
4. What does “prime” mean?

2. Factoring Polynomials Completely
Monday, February 26, 2018
Thursday September 29, 2016

3. Greatest Common Factor
No matter what type of polynomial you are factoring, you always factor out the GCF first!

4. Special Binomials Difference of squares: Ex: 4x2 – 9 Sum of cubes:
Difference of cubes:
Ex: x3 – 8

5. Uncover the mystery of factoring complex trinomials!
Factoring Fanatic
Uncover the mystery of factoring complex trinomials!

6. Once you have completed your Tic Tac– WHERE’S the ANSWER?
Use the “a” coefficient as the numerator of two fractions. Use the results in quadrants I and IV as the two denominators.
Reduce the fractions.
The numerator is your coefficient for x in your binominal and the denominator is the constant term.
EXAMPLE: If you get the fractions 1 2 and 3 −5 , your answer would be (x + 2) (3x – 5).

7. EXAMPLES
X2 – X - 12
-12 ? -1
What 2 numbers complete the Tic Tac?
Since a = 1, put a 1 in for the numerator in two fractions.
-12 3 -1 -4
You found 3 and -4. These are the denominators for the two fractions. Your fractions are 1/3 and –1/4
Your answer is (x + 3) (x – 4).

8. EXAMPLES
2X2 + 8X - 64
*Remember that sometimes a GCF should be factored out before beginning. 2(X2 + 4X – 32)
-32 ? 4
What 2 numbers complete the Tic Tac?
Since a = 1, put a 1 in for the numerator in two fractions.
-32 8 4 -4
You found 8 and -4. These are the denominators for the two fractions. Your fractions are 1/8 and –1/4.
Your answer is 2 (x + 8) (x – 4).

9. EXAMPLES
1/2X2 + 1/2X - 6
*Remember that sometimes a GCF should be factored out before beginning. 1/2(X2 + X – 12)
-12 ? 1
What 2 numbers complete the Tic Tac?
Since a = 1, put a 1 in for the numerator in two fractions.
-12 -3 1 4
You found -3 and 4. These are the denominators for the two fractions. Your fractions are –1/3 and 1/4.
Your answer is ½ (x – 3) (x + 4).

10. EXAMPLES
3X2 + 5X = 12
*Remember to re-write in standard form 3X2 + 5X - 12
-36 ? 5
What 2 numbers complete the Tic Tac?
Since a = 3, put a 3 in for the numerator in two fractions.
-36 9 5 -4
You found 9 and -4. These are the denominators for the two fractions. Your fractions are 3/9 = 1/3 and –3/4
Your answer is (x + 3) (3x – 4).

11. Perfect Square Trinomials
Ex: 𝑥 2 +12𝑥+36
Ex: : 𝑥 2 −10𝑥+25

12. Factoring by Grouping Group two terms together.
2. Factor out a GCF from each separate binomial to get a common binomial.
3. Factor out the common binomial.
Ex: x3 + 3x2 + 2x +6

13. Factoring Completely Remember, GCF first always.
Check for your Special Cases.
Sometimes you may have to
factor more than once.
Sometimes it will be Prime.

14. Assignments Classwork: Factoring Polynomials #1-15 Homework:

15. Exit Ticket 1. What do you ALWAYS do first when factoring?
2. What does it mean if the polynomial is prime?
3. How many factors can a polynomial have?