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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:**

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

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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 3rd term Right column: Find terms that add to create the coefficient on the 2nd 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 x2+ax+b: Both terms are positive**

x2+ax – b: Smaller term is negative x2 – ax – b: Larger term is negative x2 – ax + b: Both terms are negative

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**Ex: Factor x2+9x+20 Both Terms are Positive Create T-table**

Multiply: Add: 9 Plug into (x+a)(x+b) 1•20 = 20 1+20 = 21 (x+4)(x+5) 2•10 = 20 2+10 = 12 4•5 = 20 4+5 = 9 Terms: 4,5

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**Ex: Factor x2 - 12x + 32 Both Terms are negative Create T-table**

Plug into (x+a)(x+b) Multiply: Add: -12 (x-4)(x-8) -1•-32 = 32 -1-32 = -33 -2•-16 = 32 -2-16 = -18 -4•-8 = 32 -4+-8 = -12 Terms: -4,-8

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**Ex: Factor x2 + 5x - 24 Smaller term is negative Create T-table**

Plug into (x+a)(x+b) Multiply: Add: 5 (x-3)(x+8) -1•24 = -24 -1+24 =23 -2•12 = -24 -2+12 = 10 -3•8 = -24 -3+8 = 5 Terms: -3,8

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