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Objectives: Students will be able to… Write a polynomial in factored form Apply special factoring patterns 5.2: PART 1- FACTORING

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1.What 2 numbers multiply together to get 24 and have a sum of 10? 2.What is the definition of a factor of a number? WARM UP:

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The process of breaking down a product into the quantities that multiply together to get the product In essence, you are reversing the multiplication process When factoring polynomials, you are breaking it up into simpler terms; breaking it into the terms that multiply together to get the polynomial FACTORING

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The largest factor that divides evenly into a quantity In a polynomial, the GCF must be common to ALL terms. Divide out the GCF (do not drop it!!!!!!!!!!!!!!) EXAMPLES: Factor GREATEST COMMON FACTOR (GCF)

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x 2 + bx + c When a = 1, EASY!!!! Look for factor pairs of c that add up to b Be aware of signs FACTORING TRINOMIALS

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EXAMPLES: FACTOR

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Here’s another method… Factor: 2y 2 + 5y +2 Multiply a·c: 2(2) = 4 Find a product pair of a·c that adds up to b: 4, 1 Write the quadratic with the linear term as a sum of the 2 factors from the previous step: 2y 2 + 4y +1y + 2 Group the terms by 2: (2y 2 + 4y) + (1y +2) Take out the GCF of each group: 2y(y+2)+1(y+2) Regroup: (2y +1)(y +2) FACTORING WHEN a ≠1

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ax 2 + bx +c, where a ≠ 1 1. 2y 2 + 5y +22. 6n 2 -23n +7 FACTORING TRINOMIALS

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3.5d 2 -14d -34. 20p 2 -31p -9 5. 3d 2 -17d+20 EXAMPLES, CONT.

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Always look for GCF first. If it has one, factor it out and try to factor what remains in parenthesis. DO NOT DROP GCF!!!!!!! EXAMPLES: Factor FACTORING COMPLETELY

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Difference between 2 perfect squares: a 2 – b 2 = (a + b) (a – b) For example: x 2 – 9 = (x + 3)(x – 3) 4x 2 – 25 = (2x + 5)(2x -5) SPECIAL FACTORING CASES

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Perfect Square Trinomials: a 2 + 2ab + b 2 = (a +b)(a +b) = (a+ b) 2 a 2 – 2ab + b 2 = (a –b) (a- b) = (a –b) 2 For example: x 2 + 8x + 16 = (x + 4)(x +4) = (x + 4) 2 x 2 - 8x + 16 = (x - 4)(x -4) = (x - 4) 2 SPECIAL FACTORING PATTERNS, CONT. Hint…How to recognize pattern: 1.The first & last terms are perfect squares 2.The middle term is twice the product of one factor from first term & one factor from last term.

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1.n 2 + 16n +64 2.9q 2 – 12q + 4 3.4t 2 + 36t +81 4.p 2 – 49 5.16x 2 – 25 6.81- x 2 EXAMPLES: FACTOR

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1.5x 2 -20 2.6k 2 + 12k +6 3.48y 3 – 24y 2 + 3y 4.x 2 + 5x +16 5.-4x 2 – 4x + 24 6.3r 3 – 48rs 2 7.- x 2 + 11x +42 FACTOR COMPLETELY, IF POSSIBLE

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