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Factoring

Factoring. Monday, March 31 st. Factoring Simple Expressions. Example: 6x – 15. Step #1: Ask self, “What number could I evenly divide both 6x and -15 by?”. Factoring Simple Expressions. Example: 6x – 15. Step #1: Ask self, “What number could I evenly divide both 6x and -15 by?”.

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Factoring

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  1. Factoring Monday, March 31st

  2. Factoring Simple Expressions Example: 6x – 15 Step #1: Ask self, “What number could I evenly divide both 6x and -15 by?”

  3. Factoring Simple Expressions Example: 6x – 15 Step #1: Ask self, “What number could I evenly divide both 6x and -15 by?” That number appears to be 3.

  4. Factoring Simple Expressions Example: 6x – 15 Step #1: Ask self, “What number could I evenly divide both 6x and -15 by?” That number appears to be 3. Step #2: Bring the 3 out in front, and divide both the 6x and the -15 by 3.

  5. Factoring Simple Expressions Example: 6x – 15 Step #1: Ask self, “What number could I evenly divide both 6x and -15 by?” That number appears to be 3. Step #2: Bring the 3 out in front, and divide both the 6x and the -15 by 3. 3(2x – 5)

  6. Factoring Simple Expressions Factor 4x3 + 10x2 – 6x Step #1: Ask self, “What number could I evenly divide 4x3 and 10x2 and -6x by?”

  7. Factoring Simple Expressions Factor 4x3 + 10x2 – 6x Step #1: Ask self, “What number could I evenly divide 4x3 and 10x2 and -6x by?” 2x

  8. Factoring Simple Expressions Factor 4x3 + 10x2 – 6x Step #1: Ask self, “What number could I evenly divide 4x3 and 10x2 and -6x by?” 2x Step #2: Bring the 2x out in front, and divide 4x3 and 10x2 and -6x by 2x.

  9. Factoring Simple Expressions Factor 4x3 + 10x2 – 6x Step #1: Ask self, “What number could I evenly divide 4x3 and 10x2 and -6x by?” 2x Step #2: Bring the 2x out in front, and divide 4x3 and 10x2 and -6x by 2x. 2x(2x2 + 5x – 3)

  10. Factoring Simple Expressions Two solutions: –5x(5x2 + 3x – 1) 5x(–5x2–3x + 1) Factor –25x3 – 15x2 + 5x Better

  11. Factoring Quadratics

  12. Factoring Quadratics Goal: To undo FOIL Example: x2 + 3x + 2 Step #1: Set up the following factor brackets (x )(x ) Step #2: Look for two numbers that add to the x coefficient and multiply to the constant x2 + 3x + 2 Two numbers that add to 3 and multiply to 2

  13. Example: x2 + 3x + 2 (x )(x ) Step #2: Look for two numbers that add to the x coefficient and multiply to the constant x2 + 3x + 2 Two numbers that add to 3 and multiply to 2 These numbers are: +1 and +2 Step #3: Use these constants to make two binomials (x + 1)(x + 2) Step #4: Check your solution using FOIL x2 + 3x + 2

  14. Factoring Quadratics Example: x2– 3x – 10 (x )(x ) Look for two numbers that add to the x coefficient and multiply to the constant x2– 3x –10 These numbers are: -5 and +2 Use these constants to make two binomials (x – 5)(x + 2) Check your solution using FOIL

  15. Factoring Quadratics

  16. Factoring Quadratics What if there is a coefficient in front of the x? Example: 3x2– 9x – 12 Step #0: Factor out the front coefficient 3(x2– 3x – 4) Step #1: Write your factor brackets 3(x )(x ) Step #2: Look for numbers that add to -3 and multiply to -4 These are -4 and +1 Step #3: Make your binomials and check with FOIL! 3(x – 4)(x + 1)

  17. Factoring Quadratics Practice factoring the following in teams: A) x2– x – 20 B) x2– 10x + 21 C) –2x2– 10x –12 D) 4x3– 20x2 – 24x

  18. Practice Online!

  19. Page 156 #1 – 4(aceg)

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