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What is prime factorization?

What is prime factorization?. Maybe use this number as an example? -117. So final answer is: -1 x 3 2 x 13. -1 3 39. 3 13. GCF – Greatest Common Factor. Find the GCF of each set of monomials. 54, 63, 180.  9. 27a 2 b & 15ab 2 c.  3ab. 8g 2 h 2 , 20gh, 36g 2 h 3.

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What is prime factorization?

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  1. What is prime factorization? Maybe use this number as an example? -117 So final answer is: -1 x32 x 13 -1 3 39 3 13

  2. GCF – Greatest Common Factor Find the GCF of each set of monomials. 54, 63, 180  9 27a2b & 15ab2c  3ab 8g2h2, 20gh, 36g2h3  4gh

  3. 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

  4. Factor completely: • 140x3 y2 z  2 2 5 7 x x x y y z -48cd2  -1 2 2 2 2 3 c d d 55p2 – 11p4 + 44p5  11p2(5 – p2 + 4p3)

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

  6. Factoring Trinomials ax2 + bx + c • Remember to do and check each step: • Can the equation be simplified? • Is there a GCF? (then take it (factor it) out!) • Is it a special pattern: a2 – b2, a2 – 2ab + b2, a2 + 2ab + b2 look for perfect squares!!! • No special pattern, then factor! (Use grouping, ac method, illegal or diamond factoring if necessary) a2 – b2 = (a + b)(a – b) a2 – 2ab + b2 = (a – b)2 a2 + 2ab + b2 = (a + b)2 Always follow these steps!

  7. Examples 4x2 + 16  4(x2 + 4) 1) Can it be simplified? NO! 2. Is there a GCF? YES … so factor if out You’re done! 3. Is it a special pattern? NO! 4. Can it be factored any further?

  8. Another Example 4x2 – 16  4(x2 – 4) so  4(x + 2)(x – 2) 3. Is it a special pattern? YES – it’s the difference of squares 2. Is there a GCF? YES … so factor if out 1) Can it be simplified? 4. Can it be factored any further? Ta da … you’re done! Did you notice the similarity and the differences between the last 2 problems?

  9. Trinomial Examples x2 + 7x + 12  (x + 4)(x + 3) 1) Can it be simplified? You’re done! 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?

  10. Trinomial Examples #2 x2 + 3x – 10  (x + 5)(x – 2) 1) Can it be simplified? You’re done! 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?

  11. Trinomial Examples #3 2x2 – 11x + 15  (2x – 5)(x – 3) CAREFUL – there’s a number in front of the x2! 1) Can it be simplified? You’re done! 2. Is there a GCF? I’ll wait while you work it out ….. 3. Is it a special pattern? 4. Factor … use the method of YOUR choice!

  12. Trinomial Examples #4 4x2 – 18x – 10  2(2x2 – 9x – 5) CAREFUL – there’s a number in front of the x2! 1) Can it be simplified? 2. Is there a GCF?  2(x – 5)(2x + 1) 3. Is it a special pattern? I’ll wait while you work it out ….. 4. Factor … use the technique of YOUR choice! You’re done!

  13. Difference of Squares a2 – b2 (a + b)(a – b) Example: 4x2 – 25  (2x + 5)(2x – 5) 2x 2x 5 5

  14. What would you do? 48a2b2 – 12ab 6x2y – 21y2w +24xw xy – 2xz + 5y – 10z

  15. What would you do? a2 – 10a + 21 3n2 – 11n + 6 9x2 – 25 x2 – 6x – 27 = 0

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