Factoring Quadratics using X-

Box method

X- Box

factors factors

Producta∙c

Sumb

X-box Factoring• This is a guaranteed method for

factoring quadratic trinomials—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

2 0ax bx c

Solve 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

ax2 + bx + c

Last term

1st Term

Factorn

Factorm

GCF GCF

GCF

GCF

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

x

-12

4 6 -2 x

-2

+6

Solution: x2 + 4x – 12 (x + 6)(x - 2)

2x

-12

-2x

6x

Examples2. x2 - 9x + 20

20

-9

xx -4

-5

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

-4 -5

x²

20-5x

-4x

Examples3. 2x2 - 5x – 7

-14

-5

x2x -7

+1

Solution: 2x2 - 5x – 7 (2x - 7)(x + 1)

-7 2

2x²

-7

-7x

2x

Examples4. 15x2 + 7x – 2

-30

7

5x3x +

2

-1

Solution: 15x2 + 7x – 2 (3x + 2)(5x - 1)

10 -3

15x²

-2-3x

10x

• 3x2 - 13x – 10• 6x2 + x – 2• 4x2 + 9x + 2

You Try