1. Warm-Up: September 22, 2015 Simplify

2. Homework Questions?

3. Factoring Polynomials
Section P.5

4. Factoring
Factoring is the process of writing a polynomial as the product of two or more polynomials.
Prime polynomials cannot be factored using integer coefficients.
Factor completely means keep factoring until everything is prime

5. Methods of Factoring Greatest common factor
Difference of two perfect squares
Perfect-square trinomials
Factoring x2 + bx + c (big X)
Factoring ax2 + bx + c (big X)
Factor by grouping – use with 4 terms
Sum and difference of perfect cubes

6. Factoring out greatest common factor
Find the greatest common factor (GCF) of all terms.
Divide each term by the greatest common factor.
Write the GCF outside parenthesis, with the rest of the divided terms added together inside
3a2 – 12a
3a is the GCF

7. You-Try #1: Factor
a. 18x3 + 27x2 b. x2(x + 3) + 5(x + 3)

8. Warm-Up: September 24, 2012 Simplify

9. Factor by Grouping Works with an even number of terms.
Split the terms into two groups.
Factor each group separately using GCF.
If factor by grouping is possible, the part inside parentheses of each group will be the same.
Treat the parentheses as common factors to finish factoring.

10. Example 2: Factor

11. You-Try #2: Factor

12. Factoring x2 + bx + c c r s b Look for integers r and s such that:
r × s = c
r + s = b c b r s

13. Example 3

14. You-Try #3

15. September 18, 2013
Pick up a review worksheet and start working on it immediately in your assigned seat.
You have until the end of class to complete it
Have your homework out for Mr. Szwast to check.
If you have questions on the homework due tomorrow, ask after Mr. Szwast checks today’s homework

16. Warm-Up: September 19, 2013
Factor each expression:

17. You-Try #3

18. Factoring ax2 + bx + c Look for integers r and s such that: r × s = ac
r + s = b
Divide r and s by a, then reduce fractions
In your factors, any remaining denominator gets moved in front of the x ac b r s

19. Example 4

20. You-Try #4

21. Factoring Perfect Square Trinomials
Let A and B be real numbers, variables, or algebraic expressions,
1. A2 + 2AB + B2 = (A + B)2
2. A2 – 2AB + B2 = (A – B)2

22. Example 7
Factor: 16x2 – 56x + 49

23. You-Try #7
Factor: x2 + 14x + 49

24. Difference of Two Perfect Squares

25. Warm-Up: September 20, 2013 Factor Completely

26. Homework Questions?

27. Factoring the Sum and Difference of 2 Cubes
64x3 – 125 = (4x)3 – 53
= (4x – 5)((4x)2 + (4x)(5) + 52)
= (4x – 5)(16x2 + 20x + 25)
A3 – B3 = (A – B)(A2 + AB + B2)
x3 + 8 = x3 + 23
= (x + 2)( x2 – x·2 + 22)
= (x + 2)( x2 – 2x + 4)
A3 + B3 = (A + B)(A2 – AB + B2)
Example
Type

28. Example 8

29. You-Try #8

30. A Strategy for Factoring a Polynomial
If there is a common factor, factor out the GCF.
Determine the number of terms in the polynomial and try factoring as follows:
If there are two terms, can the binomial be factored by one of the special forms including difference of two squares, sum of two cubes, or difference of two cubes?
If there are three terms, is the trinomial a perfect square trinomial? If the trinomial is not a perfect square trinomial, try factoring using the big X.
If there are four or more terms, try factoring by grouping.
Check to see if any factors with more than one term in the factored polynomial can be factored further. If so, factor completely.

31. Factoring Flowchart Factor out GCF Count number of terms 4 2
Check for:
Difference of perfect squares
Sum of perfect cubes
Difference of perfect cubes
Factor by
Grouping 3
Check for perfect square trinomial
Use big X factoring
Check each factor to see if it can be factored further

32. Assignment
Page 53 #1-75 Odd

33. In Exercises 1-10, factor out the greatest common factor.
In Exercises 11-16, factor by grouping.
In Exercises 17-30, factor each trinomial, or state that the trinomial is prime.

34. In Exercises 17-30, factor each trinomial, or state that the trinomial is prime.
In Exercises 31-40, factor the difference of two squares.

35. In Exercises 41-48, factor any perfect square trinomials, or state that the polynomial is prime.
In Exercises 49-56, factor using the formula for the sum or difference of two cubes.
In Exercises 57-84, factor completely, or state that the polynomial is prime.

36. Quiz P.1-P.4
Clear everything off of your desk except a pen/pencil, eraser.
If you appear to be talking while any quizzes are out, you will receive a zero.
If you appear to be looking at anyone else’s quiz, or allowing anyone to look at your quiz, you will receive a zero.
When finished, turn in your quiz and work on the homework (questions will be on the board).

37. Homework Questions?