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Ch. 5.4: Factoring (PART 1)

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GCF: Pull common term out from all terms Ex: Pull out 2x Pull out 3 Pull out 6xy

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Difference of squares: Ex: Take the square root of the two terms and plug them into the equation above To simplify exponents, divide by 2

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Trinomials with a coefficient of 1 Make a T-table to the right of the problem Left column: Find terms that multiply to create the coefficient on the 3 rd term Right column: Find terms that add to create the coefficient on the 2 nd term Find the multiples (a and b) that make both columns true Plug them in as (x+a)(x+b) To check, FOIL your answer

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Helpful hints x 2 +ax+b: Both terms are positive x 2 +ax – b: Smaller term is negative x 2 – ax – b: Larger term is negative x 2 – ax + b: Both terms are negative

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Ex: Factor x 2 +9x+20 Both Terms are Positive Create T-table Multiply: 20 Add: 9 120 = 201+20 = 21 210 = 202+10 = 12 45 = 20 4+5 = 9 Terms: 4,5 Plug into (x+a)(x+b) (x+4)(x+5)

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Ex: Factor x 2 - 12x + 32 Both Terms are negative Create T-table Multiply: 32 Add: -12 -1-32 = 32 -1-32 = -33 Terms: -4,-8 Plug into (x+a)(x+b) (x-4)(x-8) -2-16 = 32-2-16 = -18 -4-8 = 32-4+-8 = -12

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Ex: Factor x 2 + 5x - 24 Smaller term is negative Create T-table Multiply: -24 Add: 5 -124 = -24-1+24 =23 Terms: -3,8 Plug into (x+a)(x+b) (x-3)(x+8) -212 = -24-2+12 = 10 -38 = -24-3+8 = 5

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