Factoring Quadratics using X-Box

method and Factor by Grouping

Factoring Quadratics using X-Box

method and Factor by Grouping

Bell Ringer:

Homework!• Score out of 26• Divide by 2.6

X- Marks the Spot

factors factors

Producta∙c

Sumb

Solve using factoring by grouping

Example: Factor 3x2 -13x -10

-13

(3)(-10)=

-30

-15 2

-10

(3x2-15x)+(2x-

10)

=3x(x-5)+2(x-5)

=(x-5)(3x+2)

-15x+2x

3x2

-13x=

-15x+2x

1. Plug and solve values of our “X” 2. Substitute new factors in for bx

3. Solve by grouping!

4. Check answer:

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

(x-5)(3x+2)

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

ExamplesExamplesFactor 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

ExamplesExamples2. x2 - 9x + 20

20

-9

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

-4 -5

x2-4x-5x+20

=(x2-4x)+(-5x+20)

=x(x-4)-5(x-4)

=(x-4)(x-5)

ExamplesExamples3. 2x2 - 5x – 7

-14

-5

x

2x -7

+1

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

-7 2

2x²

-7

-7x

2x

ExamplesExamples4. 15x2 + 7x – 2

-30

7

5x

3x +2

-1

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

10 -3

15x²

-2-3x

10x

• 2x2 +3x –9

• 6x2 + x – 2

• 4x2 + 9x + 2

You TryYou Try

Partner Activity!• On the front side of your Factoring Practice are your

questions. On the back side is the answer key for your partner.

• Work on your own Factoring Practice worksheet and when you want to check your answer, do so with your partner.

• Remember the purpose of this activity is to help each other to be able to solve the problems. Be good teachers! (Do not just give them the answers)

• Work on for the time given and get as far as you can!