X-box Factoring

X-box Factoring

X- Box

3 -9

Product

Sum

X-box FactoringX-box Factoring• This is a guaranteed method for factoring

quadratic equations—no guessing necessary!

• We will learn how to factor quadratic equations using the x-box method

• Background knowledge needed:

– Basic x-solve problems

– General form of a quadratic equation

– Dividing a polynomial by a monomial using the box method

Factor the x-box wayExample: Factor 3x2 -13x -10

-13

(3)(-10)=

-30

-15 2

-10

-15x

2x

3x2

x -5

3x

+2

3x2 -13x -10 = (x-5)(3x+2)

Factor the x-box way

Middleb=m+

nSum

Product

ac=mnm n

First and Last

Coefficients

y = ax2 + bx + c

Last term

1st Term

Factorn

Factorm

Base 1 Base 2

GCF

Height

ExamplesExamplesFactor using the x-box method.1. x2 + 4x – 12

a) b)

x -12

4 6 -2

x2 6x

-2x -12

x

-2

+6

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

Examples continuedExamples continued

2. x2 - 9x + 20

a) b) 20

-9

x2 -4x

-5x 20

x

x -4

-5

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

-4 -5