1. Warm-Up
Factor the following expressions by pulling out things that each term has in common:
4x3 + 8x2 + 12xz
9x2y3 + 3xy2 + 27xy4

2. X-box Factoring

3. Standard
Students apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials.
Objective: We will use the x-box method to factor trinomials.

4. Factor the x-box way
We are going to factor trinomials like 3x2 + 27x + 60 using the X-Box method.
Step 1: Write the polynomial in standard form.
Step 2: Factor all common factors in the trinomial.
Step 3: Use the X method.
Step 4: Write your answer.
Step 5: Check your answer by distributing

5. First and Last Coefficients
Factor the x-box way
y = ax2 + bx + c
Product
ac=mn
First and Last Coefficients n m
Middle
b=m+n
Sum

6. Examples Factor using the x-box method. 1. x2 + 4x – 12
-12 4 6 -2
Solution: x2 + 4x – 12 = (x + 6)(x - 2)

7. Examples continued 2. x2 - 9x + 20 20 -9
Solution: x2 - 9x + 20 = (x - 4)(x - 5)

8. You try…
Factor: x2 – 6x + 5
Answer: (x – 1)(x – 5)

9. Extra Practice Factor 1. x2 + 6x + 5 (x + 5)(x + 1) 2. r2 – 12r + 35