RULES FOR FACTORING Step 1: CMF Step 2: Binomial? DOTS?

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Presentation transcript:

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 (x2 – 2) 3 (x2 – 2x + 6) 10x3 + 15x2 – 5x = 5x (2x2 + 3x – 1)

Difference Of Two Squares D.O.T.S. Difference Of Two Squares Perfect Squares Difference means subtract x2 9 9x2 So, examples of DOTS: y2 16 25y2 a2 49 81x2y2 x2 – 16 b6 100 4x4y6 or 4a2 – 25b2

D.O.T.S. FLASH CARDS Is it DOTS? x2 – y2 D

D.O.T.S. FLASH CARDS Is it DOTS? a2 – 9 D

D D.O.T.S. 6m2 – 81 FLASH CARDS Is it DOTS? Why not? 6 IS NOT A PERFECT SQUARE!

D D.O.T.S. 4b2 + 25 FLASH CARDS Is it DOTS? Why not? THIS IS A SUM OF 2 SQUARES.

D.O.T.S. FLASH CARDS Is it DOTS? 49b2 – 100c4 D

Difference Of Two Squares 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) Example: x2 – 16 = (x + 4) (x – 4)

Difference Of Two Squares D.O.T.S. Difference Of Two Squares 4a2 – 25b2 = (2a + 5b) (2a – 5b) b2 – 49 = (b + 7) (b – 7) 9x2y2 – 64b6 = (3xy + 8b3) (3xy – 8b3)

P.S.T. Perfect Square Trinomial How to identify: x2 + 6x + 9 x 3x 3 ☺1st & last term must be perfect squares YES! x2 + 6x + 9 ☺Square root of the first ? ☺Square root of the last x 3x 3 ☺Multiply them ☺Double the result ☺Is it the same as the middle term?(disregard sign)

PST THIS IS A P.S.T. Perfect Square Trinomial How to identify: ☺1st & last term must be perfect squares x2 + 6x + 9 THIS ☺Square root of the first ? ☺Square root of the last x 3x 3 IS ☺Multiply them A PST ☺Double the result ☺Is it the same as the middle term?(disregard sign)

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 WAY DO YOU KNOW WHY?

D.O.T.S. FLASH CARDS Is it PST? x2 + 20x + 40 NO WAY DO 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

What would make this a PST? D.O.T.S. FLASH CARDS What would make this a PST? ±12x x2 _____ + 36

What would make this a PST? D.O.T.S. FLASH CARDS What would make this a PST? ±36xy 4x2 _______ + 81y2

What would make this a PST? D.O.T.S. FLASH CARDS What would make this a PST? x2 – 6x ____ + 9

Perfect Square Trinomial Square root of the first P.S.T. Perfect Square Trinomial How to factor x2 + 6x + 9 Square root of the first (x + 3) Sign of the second term 2 Square root of the last Quantity squared

Perfect Square Trinomial Square root of the first P.S.T. Perfect Square Trinomial How to factor 4m2 – 20m + 25 Square root of the first (2m – 5) Sign of the second term 2 Square root of the last Quantity squared

5x2 + 10xy 5x(x + 2y) FLASH CARDS Factoring Practice RECALL STEPS! 1. CMF 2. BINOMIAL? DOTS 5x(x + 2y) 3. TRINOMIAL PST GUESS

x2 – 9y2 (x + 3y)(x – 3y) FLASH CARDS Factoring Practice RECALL STEPS! 1. CMF 2. BINOMIAL? DOTS (x + 3y)(x – 3y) 3. TRINOMIAL PST GUESS

4x2 – 28x + 49 (2x – 7)2 FLASH CARDS Factoring Practice RECALL STEPS! 1. CMF 2. BINOMIAL? DOTS (2x – 7)2 3. TRINOMIAL PST GUESS

a2 – 2a – 15 (a – 5)(a + 3) FLASH CARDS Factoring Practice RECALL STEPS! a2 – 2a – 15 1. CMF 2. BINOMIAL? DOTS (a – 5)(a + 3) 3. TRINOMIAL PST GUESS

FLASH CARDS Solving Equations 2x3 + 8x2 – 42x = 0 2x(x2 + 4x – 21) = 0 Set equal to zero: Already is! Factor left side: 2x(x2 + 4x – 21) = 0 2x(x + 7)(x – 3) = 0 More Factoring?? Factors = to 0: 2x= 0 or x + 7 = 0 or x – 3 = 0 Solve equations: x= 0 or x = -7 or x = 3