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What is prime factorization? Maybe use this number as an example? -117 -1 3 39 3 13 So final answer is: -1 x 3 2 x 13

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GCF – Greatest Common Factor Find the GCF of each set of monomials. 54, 63, 180 9 9 27a 2 b & 15ab 2 c 3ab 8g 2 h 2, 20gh, 36g 2 h 3 4gh

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Relatively Prime Define relatively prime, then give an example. If two or more integers or monomials have a GCF of 1, then they are said to be relatively prime. Example: 21m and 25b

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Factor completely: 140x 3 y 2 z -48cd 2 55p 2 – 11p 4 + 44p 5 -1 2 2 2 2 3 c d d 2 2 5 7 x x x y y z 11p 2 (5 – p 2 + 4p 3 )

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Factor completely: 12ax + 3xz + 4ay + yz (3x + y) (4a + z) Since all terms do not have a common factor, use grouping: (12ax + 3xz) + (4ay + yz) 3x (4a + z)+ y (4a + z)

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Factoring Trinomials ax 2 + bx + c Remember to do and check each step: 1)Can the equation be simplified? 2)Is there a GCF? (then take it (factor it) out!) 3)Is it a special pattern: a 2 – b 2, a 2 – 2ab + b 2, a 2 + 2ab + b 2 look for perfect squares!!! 4)No special pattern, then factor! (Use grouping, ac method, illegal or diamond factoring if necessary) Always follow these steps! a 2 – b 2 = (a + b)(a – b) a 2 – 2ab + b 2 = (a – b) 2 a 2 + 2ab + b 2 = (a + b) 2

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Examples 4x 2 + 16 4(x 2 + 4) 1) Can it be simplified? 2. Is there a GCF?YES … so factor if out 3. Is it a special pattern? 4. Can it be factored any further? You’re done! NO!

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Another Example 4x 2 – 16 4(x 2 – 4) 1) Can it be simplified? 2. Is there a GCF?YES … so factor if out 3. Is it a special pattern? 4. Can it be factored any further? Ta da … you’re done! YES – it’s the difference of squares so 4(x + 2)(x – 2) Did you notice the similarity and the differences between the last 2 problems?

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Trinomial Examples x 2 + 7x + 12 (x + 4)(x + 3) 1) Can it be simplified? 2. Is there a GCF? 3. Is it a special pattern? 4. Factor … what are the factors of the last term that add up to the middle term? You’re done!

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Trinomial Examples #2 x 2 + 3x – 10 (x + 5)(x – 2) 1) Can it be simplified? 2. Is there a GCF? 3. Is it a special pattern? 4. Factor … what are the factors of the last term that add up to the middle term? You’re done!

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Trinomial Examples #3 2x 2 – 11x + 15 (2x – 5)(x – 3) 1) Can it be simplified? 2. Is there a GCF? 3. Is it a special pattern? 4. Factor … use the method of YOUR choice! You’re done! CAREFUL – there’s a number in front of the x 2 ! I’ll wait while you work it out …..

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Trinomial Examples #4 4x 2 – 18x – 10 2(2x 2 – 9x – 5) 1) Can it be simplified? 2. Is there a GCF? 3. Is it a special pattern? 4. Factor … use the technique of YOUR choice! You’re done! CAREFUL – there’s a number in front of the x 2 ! I’ll wait while you work it out ….. 2(x – 5)(2x + 1)

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Difference of Squares a 2 – b 2 (a + b)(a – b) Example: 4x 2 – 25 (2x + 5)(2x – 5) 2x 2x 5 5

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What would you do? 48a 2 b 2 – 12ab 6x 2 y – 21y 2 w +24xw xy – 2xz + 5y – 10z

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What would you do? a 2 – 10a + 21 3n 2 – 11n + 6 9x 2 – 25 x 2 – 6x – 27 = 0

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5.4 F ACTORING P OLYNOMIALS Algebra II w/ trig. 1. GCF: Greatest Common Factor - it may be a constant, a variable, of a combination of both (3, X, 4X)

5.4 F ACTORING P OLYNOMIALS Algebra II w/ trig. 1. GCF: Greatest Common Factor - it may be a constant, a variable, of a combination of both (3, X, 4X)

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