1. Unit 3.1 Rational Expressions, Equations, and Inequalities
Intro: Factoring Review
Objectives:
To factor a monomial from a polynomial
To factor trinomials of the form ax2 + bx + c
To factor higher degree polynomials by grouping
To factor sum or difference of cubes

2. Finding the Greatest Common Factor
GCF - The highest number that divides exactly into two or more numbers. 

3. Example 1: Finding the Greatest Common Factor
-x5 + 9x3
5x3 + 25x2 + 45x
List the prime factors of each term. Identify the factors common to all terms.
Are there any common factors? How about -1?

4. Factoring by Grouping
First group the two terms with the highest degrees. If that doesn’t work, try another grouping. Your goal is to find a common binomial factor 

5. Example 2: Factoring by Grouping
3n3 – 12n2+ 2n – 8
8x3 + 14x2 + 20x + 35
Factor out the GCF of each group of two terms

6. Factoring Quadratic Trinomials when a = 1. ax2 + bx + c
To factor a trinomial of the form ax2 + bx + c as a product of binomials:
You want the factors in the form (x + m) (x + n) for some numbers m and n.
You will want to find two numbers that mult. to equal the constant term ‘c’ and also add to equal ‘b’

7. Example 3: Factoring Quadratic Trinomials when a = 1. ax2 + bx + c
This polynomial appears to be missing the “bx” term. Rewrite the polynomial with a coefficient of 0 with the variable x.
Identify the pair of factors of -16 that have a sum of 0.
SAME FACTORS
_____ × _____ = -16
_____ + _____ = 0
Identify the pair of factors of 24 that have a sum of 11.
SAME FACTORS
_____ × _____ = 24
_____ + _____ = 11
x2 + 11x + 24
x2 + 2x – 15
x2 – 16
Identify the pair of factors of -15 that have a sum of 2.
SAME FACTORS
_____ × _____ = -15
_____ + _____ = 2

8. Factoring Quadratic Trinomials when a ≠ 1. ax2 + bx + c
To factor a trinomial of the form ax2 + bx + c
Find two numbers that mult. to equal ‘ac’ and add to equal ‘b’
Rewrite the middle term ‘bx’ with the new terms
Factor the first two and last two terms separately (factor by grouping)
If you have done this correctly, our two new terms should clearly have a common factor.

9. Example 4: Factoring Quadratic Trinomials when a ≠ 1. ax2 + bx + c
5x2 + 11x + 2
2x2 - 13x - 7
Step 1: Find factors of ac that have a
sum of b.
Since ac = 10 and b = 11, find positive factors of 10 that have sum 11
_______ × _______ = 10
_______ + _______ = 11
Step 1: Find factors of ac that have a
sum of b.
Since ac = -14 and b = -13, find factors of -14 that have sum -13
_______ × _______ = -14
_______ + _______ = -13
Step 2: To factor the trinomial, use the factors you found to rewrite bx (order is not important)
Step 3: Factor the first two and last two terms separately
(if we have done this correctly, our two new terms should have a common factor)

10. 1st check for GCF – Factor (divide) out the greatest common factor
If the leading coefficient is negative, factor out a -1 with the GCF
3 terms
Quadratic Trinomial
ax2 + bx +c
when a = 1
3 terms
Quadratic Trinomial
ax2 + bx +c
when a ≠ 1
4 terms
Grouping