1. Warm up
Factor:
1. p2 + 13p – 30
2. a2 – 12a – 45
3. x2 – 9x – 8

2. Lesson 5-9 Factoring Pattern for ax2 + bx + c
Objective: To factor general quadratic trinomials with integral coefficients.

3. Trial & Error Method Example: 3x2 + 2x - 8
List the factors of the a term and the c term. a = 3 factors: 1 and 3 c = -8 factors: 2 and 4 or 1 and 8
Write down two sets of parentheses with empty spaces like this: ( x    )( x    )

4. Trial & Error Method 3x2 + 2x - 8
Fill the spaces in front of the x's with a pair of possible factors of the a value. There is only one possibility for our example: (3x   )(1x   )
Fill in the two spaces after the x's with a pair of factors for the constant. Let's say we choose (3x  8)(x  1).

5. Trial & Error Method 3x2 + 2x - 8
Decide what signs should be between the x's and the numbers. Here's a guide: If ax2 + bx + c then (x + h)(x + k) If ax2 - bx - c or ax2 + bx - c then (x - h)(x + k)
If ax2 - bx + c then (x - h)(x – k) For our example 3x2 + 2x - 8 so (x - h)(x + k) (3x + 8)(x - 1)

6. Trial & Error Method 3x2 + 2x - 8
Test your choice by multiplying (use FOIL) the two parentheses together.
Swap out your choices if necessary. In our example, let's try 2 and 4 instead of 1 and 8: (3x + 2)(x - 4)
Reverse the order if necessary. Let's try moving the 2 and 4 around: (3x + 4)(x - 2)

7. Trial & Error Method 3x2 + 2x - 8
Double-check your signs if necessary. We're going to stick with the same order, but swap which one has the subtraction: (3x - 4)(x + 2)
This finally foils to the correct trinomial.

8. Triple Play or “Magic” Method
Example: 4x2 + 5x + 1
Multiply the a term (4 in the example) by the c term (1 in this example).
4•1 = 4
Find the two numbers whose product is this number (4) and whose sum is equal to the b term (5). 1•4 = 4   1 + 4 = 5

9. Triple Play or “Magic” Method
Take these two numbers (which we will call h and k) and substitute them into this expression: (ax + h)(ax + k)      a (4x + 4)(4x + 1)      4

10. Triple Play or “Magic” Method
Look to see which one of the two parenthesis terms in the numerator is evenly divisible by a {in this example it is (4x + 4)}. Divide this term by a and leave the other one as is. (4x + 4)(4x + 1)      8 Answer:(x + 1)(4x + 1)

11. Triple Play or “Magic” Method
Take the GCF (if any) out of either or both parentheses. (x + 1)(4x + 1)

12. Try
2b2 + 13b – 24
5y2 – 17y + 6
3k2 – 8k – 35