RULES FOR FACTORING

Step 1: CMF

Step 2: Binomial?

DOTS?

Step 3: Trinomial?PST?Guess Method

RULES FOR FACTORING

REVIEW OF CMF

6x2 – 12 = 6

3x2 – 6x + 18 = 3

10x3 + 15x2 – 5x = 5x

(x2 – 2)

(x2 – 2x + 6)

(2x2 + 3x – 1)

D.O.T.S.Difference Of Two Squares

Perfect Squares

x2

y2

a2

b6

9

16

49

100

9x2

25y2

81x2y2

4x4y6

Differencemeans subtract

So, examplesof DOTS:

x2 – 16or

4a2 – 25b2

D.O.T.S.FLASH CARDS

Is it DOTS?

x2 – y2

D.O.T.S.FLASH CARDS

Is it DOTS?

a2 – 9

D.O.T.S.FLASH CARDS

Is it DOTS?

6m2 – 81

Why not?6 IS NOT A PERFECT SQUARE!

D.O.T.S.FLASH CARDS

Is it DOTS?

4b2 + 25

Why not?THIS IS A SUM OF 2 SQUARES.

D.O.T.S.FLASH CARDS

Is it DOTS?

49b2 – 100c4

D.O.T.S.Difference Of Two Squares

DOTS always factors the same way.

(Square root of the first + square root of the last) times(Square root of the first – square root of the last)

x2 – 16 =

Example:

(x + 4) (x – 4)

D.O.T.S.Difference Of Two Squares

4a2 – 25b2 = (2a + 5b)

b2 – 49 = (b + 7)

9x2y2 – 64b6 = (3xy + 8b3)

(2a – 5b)

(b – 7)

(3xy – 8b3)

P.S.T.Perfect Square Trinomial

x2 + 6x + 9

How to identify:

☺Square root of the first

x☺Square root of the last

3☺Multiply them3x

☺Double the result

☺Is it the same as the middle term?(disregard sign)

☺1st & last term must be perfect squares

?

YES!

P.S.T.Perfect Square Trinomial

x2 + 6x + 9

How to identify:

☺Square root of the first

x☺Square root of the last

3☺Multiply them3x

☺Double the result

☺Is it the same as the middle term?(disregard sign)

☺1st & last term must be perfect squares

?

THIS

IS A PST

D.O.T.S.FLASH CARDS

Is it PST?

x2 – 10x + 25

U BETCHA

D.O.T.S.FLASH CARDS

Is it PST?

x2 – 10x – 25

NO WAYDO YOU KNOW WHY?

D.O.T.S.FLASH CARDS

Is it PST?

x2 + 20x + 40

NO WAYDO YOU KNOW WHY?

D.O.T.S.FLASH CARDS

Is it PST?

9m2 + 42m + 49

U BETCHA

D.O.T.S.FLASH CARDS

Is it PST?

x2 + 16xy + 64y2

U BETCHA

D.O.T.S.FLASH CARDS

What would make this a PST?

x2 _____ + 36±12x

D.O.T.S.FLASH CARDS

What would make this a PST?

4x2 _______ + 81y2±36xy

D.O.T.S.FLASH CARDS

What would make this a PST?

x2 – 6x ____+ 9

P.S.T.Perfect Square Trinomial

x2 + 6x + 9

How to factor

Square root of the first

(xSquare root of the last

2Sign of the second term 3)

Quantity squared

+

P.S.T.Perfect Square Trinomial

4m2 – 20m + 25

How to factor

Square root of the first

(2mSquare root of the last

2Sign of the second term 5)

Quantity squared

–

FLASH CARDSFactoring Practice

5x2 + 10xyRECALL STEPS!

CMF

BINOMIAL?

TRINOMIAL

GUESS

5x(x + 2y)DOTS

PST

1.

2.

3.

FLASH CARDSFactoring Practice

x2 – 9y2RECALL STEPS!

CMF

BINOMIAL?

TRINOMIAL

GUESS

(x + 3y)(x – 3y)DOTS

PST

1.

2.

3.

FLASH CARDSFactoring Practice

4x2 – 28x + 49RECALL STEPS!

CMF

BINOMIAL?

TRINOMIAL

GUESS

(2x – 7)2DOTS

PST

1.

2.

3.

FLASH CARDSFactoring Practice

a2 – 2a – 15RECALL STEPS!

CMF

BINOMIAL?

TRINOMIAL

GUESS

(a – 5)(a + 3)DOTS

PST

1.

2.

3.

FLASH CARDSSolving Equations2x3 + 8x2 – 42x = 0

Set equal to zero:Factor left side:

Factors = to 0:

Solve equations:

Already is!2x(x2 + 4x – 21) = 0

More Factoring?? 2x(x + 7)(x – 3) = 0

2x= 0 or x + 7 = 0 or x – 3 = 0

x= 0 or x = -7 or x = 3