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2.3 Part 1 Factoring

2.3 Part 1 Factoring. 10/29/2012. What is Factoring?. It is finding two or more numbers or algebraic expressions, that when multiplied together produce a given product. Ex. Factor 6: 2 • 3 Factor 2x 2 + 4: 2 • (x 2 +2) Factor x 2 +5x + 6: (x+2)•(x+3).

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2.3 Part 1 Factoring

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  1. 2.3 Part 1Factoring 10/29/2012

  2. What is Factoring? It is finding twoormorenumbers or algebraicexpressions,that whenmultipliedtogetherproduce a givenproduct. Ex. Factor 6: 2 • 3 Factor 2x2 + 4: 2 • (x2 +2) Factor x2 +5x + 6: (x+2)•(x+3)

  3. Type 1 ProblemsFactoring Quadratic equations in Standard formy = ax2 + bx +cwhen a = 1and when a > 1

  4. The Big “X”method Factor: x2 + bx + c Note: a = 1 Think of 2 numbers that Multiply to c and Add to b multiply c #1 #2 b add Answer: (x ± #1) (x ± #2)

  5. Factor: x2 + 8x + 15 Think of 2 numbers that Multiply to 15 and Add to 8 3 x 5 = 15 3 + 5 = 8 15 3 5 multiply 8 c #1 #2 b Answer: (x + 3) (x + 5) add

  6. Factor: x2-6x + 8 Think of 2 numbers that Multiply to 8 and Add to -6 -4 x -2 = 8 -4 + -2 = -6 8 -4 -2 multiply -6 c #1 #2 b Answer: (x - 4) (x - 2) To check: Foil (x – 4)(x – 2) and see if you get x2-6x+8 add

  7. Factor: x2+ 8x - 9 Think of 2 numbers that Multiply to -9 and Add to 8 9 x -1 = -9 9 + -1 = 8 -9 -9 8 8 multiply c #1 #2 b Answer: (x - 9) (x + 8) add

  8. Factor: ax2 + bx + c Note: a > 1 The Big “X”method Think of 2 numbers that Multiply to a•cand Add to b multiply a a Simplify like a fraction if needed a•c Simplify like a fraction if needed #1 #2 b add Answer: Write the simplified answers in the 2 ( ) as binomials. Top # is coefficient of x and bottom # is the 2nd term

  9. Factor: 3x2 + 7x + 2 Think of 2 numbers that Multiply to 6 and Add to 7 6 x 1 = 6 6 + 1 = 7 1 3•2 = 6 3 3 Simplify like a fraction . ÷ by 3 6 1 2 multiply 7 a a a•c #1 #2 b Answer: (x + 2) (3x + 1) add

  10. Factor: 4x2-16x -9 Think of 2 numbers that Multiply to -36 and Add to -16 -18 x 2 = -36 -18 + 2 = -16 4(-9) = -36 2 4 4 2 Simplify like a fraction . ÷ by 2 Simplify like a fraction . ÷ by 2 -18 2 1 -9 multiply -16 a a a•c #1 #2 b Answer: (2x - 9) (2x + 1) add

  11. Type 2 ProblemsFactoring Quadratic equations written as Difference of 2 Squares.

  12. Difference of Two Squares Pattern (a + b) (a – b) = a2– b2 In reverse, a2– b2 gives you (a + b) (a – b) Examples: 1. x2 – 4 = x2 – 22 = (x + 2) (x – 2) 2. x2 – 144 =(x + 12) (x – 12) 3. 4x2 – 25 = (2x + 5) (2x – 5)

  13. If you can’t remember that, you can still use the big X method. Factor: x2 – 4 Ex. x2 + 0x– 4 Think of 2 numbers that Multiply to -4 and Add to 0 2 x -2 = -4 2 + -2 = 0 -4 2 -2 0 Answer: (x + 2) (x - 2)

  14. x2 + 0x– 144 Ex. x2 – 144 Think of 2 numbers that Multiply to -144 and Add to 0 12 x -12 = -144 12 + -12 = 0 -144 12 -12 0 Answer: (x + 12) (x - 12)

  15. Factor: 4x2-25 4x2+0x -25 Think of 2 numbers that Multiply to -100 and Add to 0 -10 x 10 = -100 -10 + 10 = 0 4(-25) = -100 2 4 4 2 Simplify like a fraction . ÷ by 2 Simplify like a fraction . ÷ by 2 10 -10 5 -5 0 Answer: (2x - 5) (2x + 5)

  16. Type 3 ProblemsFactoring Quadratic equations by taking out the Greatest Common Factor

  17. Factor y = x2 – 6x 1. Find the GCF. GCF = x 2. Factor the GCF out. Think reverse “distributive prop.” y = x (x – 6)

  18. Factor y = -8x2 + 18 1. Find the GCF. GCF = -2 Why -2 and not 2 you ask? Wait for the next step. 2. Factor the GCF out. y = -2 (x2 - 9) Answer: So we can have the difference of 2 squares pattern y = 2 (-x2 + 9) Not Difference of 2 Squares 3. Factor what’s in the ( ) since it follows the difference of 2 square pattern. y = -2(x – 3)(x + 3)

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