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FACTORING

FACTORING. 11/29/2012. Warm Up Find the square or square root of each. 3 2 16 2 (-12) 2 (2x) 2 (x+1) 2 (3x-4) 2. 7) √100 8) √225 9) √x 2 10) √9x 2 11) √(x-3) 2 12) √x 2 + 2x + 1. Term. 1 x x² 4x³ x²y³.  Monomial Binomial x + 1 3x 4 y + y 2 z Trinomial

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FACTORING

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  1. FACTORING 11/29/2012

  2. Warm UpFind the square or square root of each. • 32 • 162 • (-12)2 • (2x)2 • (x+1)2 • (3x-4)2 7) √100 8) √225 9) √x2 10) √9x2 11) √(x-3)2 12) √x2 + 2x + 1

  3. Term 1 x x² 4x³ x²y³  Monomial Binomial x + 1 3x4y + y2z Trinomial 5x3 – x2 + 10 Polynomial 3xyz + 3xy2z - 0.1xz - 200y + 0.5

  4. Polynomial “poly” =many “-nomial” = terms

  5. Polynomials and Operations Addition + Multiplication  x  x 2x  x 3x  x 2x  3x 5x  9x x²  x² x²  x x + x 2x + x 3x + x 2x + 3x 5x + 9x x² + x² x² + x

  6. Polynomials and Operations Addition + Multiplication  (7x)(x²)(-3x) (7x²)(x²)(7x³) 7x + x² – 3x 7x² + x² + 7x³ What if? What if?

  7. Distributive Property To multiply a term outside the parenthesis with every term inside the parenthesis Examples: 5 (1 + 2) -3p(2p2 + 3pq – 5q) (x+2)(x-2) = 5(1) + 5(2) = 5 + 10 = 15 = -3x(2y2) + -3x(3xy) + -3x(-5y) = -6x3 – 9x2y + 15xy = x(x-2) + 2(x-2) =x2 -2x + 2x -4 = x2 - 4

  8. Distributing Methods • Box Method • (x-1)(x-2) • FOIL (x-1)(x-2) F O I L x2 + x - 2x + 2 x -1 X -2

  9. Distribution Multiplication  over Addition + = 1) 3(x + 1) 2) - (x + 1) 3) -2(x + 1) 4) x( x + 1) 5) (x + 1)(x + 1) 6) (x + 1)² 7) (x + 1)³

  10. ClassworkHandout

  11. What two numbers multiplied together equals… 12x 24x 9x² • 12 • 24 • 20

  12. Factor • To break, reduce, or take a term apart into smaller terms • To rewrite as a product of two or more terms • Opposite of distribute • There are 7 main forms of factoring, which you will learn today and next week.

  13. Factor the following -32x + 2x3 x2 – 11 x + 18 x2 + 11 x + 18 x2 – 2x – 15 x2 + 2x - 15 Ms. Constanza, I forgot and I don’t know how. Can you please TEACH ME HOW TO FACTOR http://www.youtube.com/watch?v=OFSrINhfNsQ

  14. The 7 Forms of factoring Always 2 Terms 3 Terms 4 Terms Greatest Common factor (G.C.F.) Difference of two Squares Difference of two Cubes Sum of Two Cubes Perfect Square Trinomial A Quadratic Trinomial Factor by Grouping

  15. GCF Complete the factorization for each • 3x² + 15x = 3( ) • 3x² + 15x = x( ) • 3x² + 15x = 3x( ) • Which of the above factorization for 3x² + 15x do you think is best? Why?

  16. FACTOR by finding the GCFif the terms do not have a GCF, then they are relatively prime • 5x + 5 • 3x² + x • 15x² + 5x • 2x² - 18 • 6x² - 3x + 9 • x³ - 5x • 7x - 9

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