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Warm-Up. Factor the following expressions by pulling out things that each term has in common: 4x 3 + 8x 2 + 12xz 9x 2 y 3 + 3xy 2 + 27xy 4. X-box Factoring. Standard.

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Presentation Transcript
warm up
Warm-Up

Factor the following expressions by pulling out things that each term has in common:

  • 4x3 + 8x2 + 12xz
  • 9x2y3 + 3xy2 + 27xy4
standard
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
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 way1
Factor the x-box way

y = ax2 + bx + c

Product

ac=mn

First and Last Coefficients

n

m

Middle

b=m+n

Sum

examples

-12

4

Examples

Factor using the x-box method.

1. x2 + 4x – 12

6

-2

Solution: x2 + 4x – 12 = (x + 6)(x - 2)

examples continued
Examples continued

2. x2 - 9x + 20

-4-5

20

-9

Solution: x2 - 9x + 20 =(x - 4)(x - 5)

you try
You try…

Factor: x2 – 6x + 5

Answer: (x – 1)(x – 5)

extra practice
Extra Practice

Factor

1. x2 + 6x + 5

(x + 5)(x + 1)

2. r2 – 12r + 35

(r – 5)(r – 7)