Transcript Diamond and Box Factoring - Mr. Marzka's Math Class Blog

Warm-Up
Factor the following expressions by
pulling out things that each term
has in common:
1. 4x3 + 8x2 + 12xz
2. 9x2y3 + 3xy2 + 27xy4
X-box
Factoring
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.
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
Factor the x-box way
y = ax2 + bx + c
First and
Last
Coefficients
Product
ac=mn
n
m
b=m+n
Sum
Middle
Examples
Factor using the x-box method.
1. x2 + 4x – 12
6
-12
4
-2
Solution: x2 + 4x – 12 = (x + 6)(x - 2)
Examples
continued
2. x2 - 9x + 20
20
-4
-5
-9
Solution: x2 - 9x + 20 = (x - 4)(x - 5)
You try…
Factor: x2 – 6x + 5
Answer: (x – 1)(x – 5)
Extra Practice
Factor
1. x2 + 6x + 5
(x + 5)(x + 1)
2. r2 – 12r + 35
(r – 5)(r – 7)