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August 23, 2012 18g2 and 27g3 15x3 and 30x2 4x 2 and 5y3 August 23, 2012 3 2 9x - 3x + 6x 1. Find the GCF 2. "UN"distribute 3. Multiply to check August 23, 2012 A. 10y3 + 20y2 - 5y B. -12x - 8x2 C. 5x2 + 7 August 23, 2012 Factoring Trinomials Leading Coefficient of 1 *** When factorable, a trinomial will become 2 _________ ( ± )( ± ) As I mentioned yesterday, we should always look for a GCF in any polynomial. Today however, there will not be any GCFs. We are just focusing on the method we will call "EASY" TRIs August 23, 2012 Ex.1 x2 + 7x + 12 12 Step 1 : List all pairs of numbers that multiply to equal the constant, 12. Step 2 : Choose the pair that adds up to the middle coefficient, _____. Step 3 : Fill those numbers into the blanks in the binomials: (x x2 + 7x + 12 = ( x + 3)( x + 4) )( x ) August 23, 2012 Ex.2 x2 + 2x - 24 -24 Step 1 : List all pairs of numbers that multiply to equal the constant, -24. (To get -24, one number must be positive and one negative.) Step 2 : Which pair adds up to 2? Step 3 : Write the binomial factors. (x x2 + 2x - 24 = ( x - 4)( x + 6) )( x ) August 23, 2012 Ex.3 x2 - 9x + 18 18 Step 1 : List all pairs of numbers that multiply to equal the constant, 18. (Since the middle term is negative, both factors will be negative.) Step 2 : Which pair adds up to _______? Step 3 : Write the binomial factors. (x x2 - 9x + 18 = ( x - 3)( x - 6) )( x ) August 23, 2012 Now it's your turn! A. x2 + 10x + 24 B. x2 - 8x - 20 August 23, 2012 Factoring Trinomials Leading Coefficient ≠ 1 *** Again when factorable, a trinomial will become 2 _________, however it will no longer just be ( x ± )( x ± ) Again as I mentioned before, we should always look for a GCF in any polynomial. Today however, there will not be any GCFs. We are just focusing on the method we will call "TRICKY" TRIs or "Divide and Slide" August 23, 2012 Ex.1 2x2 + 13x + 15 2 · 15 = Step 1 : List all pairs of numbers that multiply to a · c. Step 2 : Still choose the pair that adds up to the middle coefficient, _____. Step 3 : TEMPORARILY Fill those numbers into the blanks in the binomials: (x x2 + 7x + 12 = ( x + 3)( x + 4) )( x ) August 23, 2012 Step 4 : The DIVIDE - DIVIDE each factor by the a value, _______. Step 5 : The SLIDE - reduce each fraction as always. SLIDE any remaining denominator in front of the x. ( x + 3 )( x + 10 ) ( x + 3 )( x + 5 ) 2 SO . . . . 2x2 + 13x + 15 = (2x + 3)(x + 5) August 23, 2012 Ex.2 3x2 - 11x - 4 3 · -4 = Step 1 : List all pairs of numbers that multiply to a · c. Step 2 : Still choose the pair that adds up to the middle coefficient, _____. Step 3 : TEMPORARILY Fill those numbers into the blanks in the binomials: (x x2 + 7x + 12 = ( x + 3)( x + 4) )( x ) August 23, 2012 Step 4 : The DIVIDE - DIVIDE each factor by the a value, _______. Step 5 : The SLIDE - reduce each fraction as always. SLIDE any remaining denominator in front of the x. ( x + 1 )( x - 12 ) ( x + 1 )( x - 4 ) 3 SO . . . . 3x2 - 11x - 4 = (3x + 1)(x - 4) August 23, 2012 Ex.3 6x2 - 13x + 6 6·6= Step 1 : List all pairs of numbers that multiply to a · c. Step 2 : Still choose the pair that adds up to the middle coefficient, _____. Step 3 : TEMPORARILY Fill those numbers into the blanks in the binomials: (x x2 + 7x + 12 = ( x + 3)( x + 4) )( x ) August 23, 2012 Step 4 : The DIVIDE - DIVIDE each factor by the a value, _______. Step 5 : The SLIDE - reduce each fraction as always. SLIDE any remaining denominator in front of the x. ( x - 4 )( x - 9 ) ( x - 2 )( x - 3 ) 3 2 SO . . . . 6x2 - 13x + 6 = (3x - 2)(2x - 3) August 23, 2012 Now it's your turn! A. 4x2 + 19x + 12 (4x + 3)(x + 4) B. 3x2 - x - 10 (3x + 5)(x - 2) August 23, 2012 Perfect Squares 1 4 9 16 25 36 49 64 81 100 121 144 a2 b2 c2 d4 e6 . . . . . x12 y20 z100 August 23, 2012 2 a -4 x2 - y2 August 23, 2012 4a2 - 25 81a2 - 1 August 23, 2012 3 2 4x + 8x - 3x - 6 August 23, 2012 Factoring Checklist 1. No matter how many terms - Check for GCF 2. 2 Terms? Is it DOTS? YES NO (a + b)(a - b) Done! 3. 3 Terms? "Easy" or "Tricky" ( ± )( ± ) 4. Grouping 4 Terms? August 23, 2012 Homework p. A30 73-119 odds SKIP 113 ADD 100