1. Section 5.4 Factoring Objectives: To find the LCM and GCF of monomials
To factor special products
To factor quadratic polynomials
To factor by grouping

2. Least Common Multiple (LCM) -
Greatest Common Factor (GCF) -The greatest integer that is a factor of each number. When variables are present you list common variables to the lowest power.
Least Common Multiple (LCM) -
The least positive integer having each number as a factor.
When variables are present you list any variable to the highest power.

3. GCF and LCM of Monomials
GCF of monomials
GCF of the coefficients
Variables portion – common variables to their lowest power
LCM of monomials
LCM of the coefficients
Variables portion – any variables to their highest power

4. GCF and LCM of Monomials
Ex 7) 48u2v2 & 6uv3w

5. GCF and LCM of Monomials
Ex 8) 8ax2 & 12a2x

6. GCF PST DoS SoS Quadratics Grouping greatest common factor
perfect square trinomial
difference of squares
sum of squares
Quadratics
Grouping

7. First rule of factoring: Always pull out what they have in common first! GCF Greatest Common Factor

8. Example 1
Factor:

9. Example 2
Factor:

10. Perfect Square Trinomials

11. How to Recognize a Perfect Square Trinomial
First term is a perfect square
Last term is a perfect square
Perfect squares are always positive
Double the product of the square roots of coefficients of the first and last terms must equal the absolute value of the middle term.

12. Examples 3 and 4
Factor:

13. Differences of Squares
**YOU CANNOT FACTOR A SUM OF SQUARES!!!!!!!

14. Examples 5 and 6
Factor:

15. Example 7
Factor:

16. Example 9
Factor:

17. Example 10
Factor:

18. Assignment
Worksheet 5.4.1

19. Quadratic Polynomial
ax2 + bx + c

20. There are four permutations of the signs in a quadratic.
x2 - 5x + 4
Templates:
+ + (x + )(x + ) sum
- + (x - )(x - ) sum
+ - (x + )(x - ) sum
- - (x + )(x - ) sum

21. Example 1
Factor:
x2 + 9x + 14 21

22. Example 2
Factor:
x2 + 2x - 15

23. Example 3
Factor:
x2 - 10x + 9 23

24. Example 4
Factor:
x2 - 10x + 24 24

25. Example 5
Factor:
x2 + 4x - 3

26. Example 6
Factor:
3 – 2z – z2

27. Example 7
Factor:
3x2 – 8x + 5

28. Example 8
Factor:
15t2 – 16t + 4

29. Example 9
Factor:
3x6 – 48x2

30. Factor by Grouping

31. Example 13
Factor:
(Rearrange with common factors first)

32. Assignment
Worksheet 5.4.2