Warm Up Find the GCF 1) 56, 26 2) 144x5wz3, 36x3z2m Factor Completely 3) 18z4 + 21z3 – 9z2 4) 3xy + 21x – 2y – 14

Divisibility Rules

Homework 

Standard Form: ax2 + bx + c Factoring Standard Form: ax2 + bx + c

Factoring is the opposite of multiplying: (x +7)(x + 3) = x2 + 10x + 21 Factoring

there are many methods we can use to get to the same answer I am going to show you two ways You decide which one you like

Method 1… We have to find a number that multiplies to the “c” term whose factors add to the “b” term (x +7)(x + 3) = x2 + 10x + 21 7 • 3 = 21 7 + 3 = 10 Some people like to organize this using an X-box, and not the gaming system

First and Last Coefficients Factor the x-box way y = ax2 + bx + c Product ac=mn First and Last Coefficients Now let’s practice Finding the m and n terms n m Middle b=m+n Sum

Now let’s Factor!!!

First and Last Coefficients Examples Factor. 1. x2 + 4x – 12 y = ax2 + bx + c Product ac=mn -12 4 First and Last Coefficients 6 -2 n m Middle b=m+n Sum Solution: x2 + 4x – 12 = (x + 6)(x - 2)

First and Last Coefficients Examples continued y = ax2 + bx + c 2. x2 - 9x + 20 Product ac=mn -4 -5 20 -9 First and Last Coefficients n m Middle b=m+n Sum Solution: x2 - 9x + 20 = (x - 4)(x - 5)

Method 2… “Undoing” the Box x2 - 7a + 6

x2 – 3x - 28

24 + 10x + x2

d2 – 6d – 27

2x2 + 6x + 4

x2 – 9

Think-Pair-Share Based on the problems we’ve done, list the steps for factoring so that someone else can do a problem using only your steps. 2. Trade papers with your partner and use their steps to factor the following problem: x2 + 4x - 32. Make sure your partner uses the same method as you!!!!

Trying out the Steps If you cannot complete the problem using only the steps written, put an arrow on the step where you stopped. Give your partner’s paper back to him. Modify the steps you wrote to correct any incomplete or incorrect steps. Finish the problem based on your new steps and give the steps back to your partner. Try using the steps again to factor: x2 - x - 56.

You Try!- Choose your own method Factor the expression: x2 + 7x + 10

You Try! Factor the expression: x2 – 2x – 24

You Try! Factor the expression: x2 – 15x + 26

You Try! Factor the expression: x2 – 6x – 27

You try!!! Factor the expression: x2 + 9x + 14