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Factoring Polynomials

Factoring Polynomials. Thursday, March 6, 2014. Greatest Common Factor. No matter what type of polynomial you are factoring, you always factor out the GCF first!. What if it’s a binomial ?. 1 st – Factor out GCF 2 nd – Difference of Squares 3 rd – Sum of Cubes

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Factoring Polynomials

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  1. Factoring Polynomials Thursday, March 6, 2014

  2. Greatest Common Factor • No matter what type of polynomial you are factoring, you always factor out the GCF first!

  3. What if it’s a binomial? • 1st – Factor out GCF • 2nd – Difference of Squares • 3rd – Sum of Cubes • 4th – Difference of Cubes

  4. Binomials continued … • Difference of squares – Ex: (4x2 – 9)  (2x + 3) (2x – 3) • Sum of cubes – Ex: 8x3 + 27  (2x +3) (4x2 – 6x + 9) • Difference of cubes – Ex: x3 – 8  (x – 2) (x2 + 2x + 4)

  5. What if it’s a trinomial? • 1st – Factor out GCF • 2nd – Perfect Square Trinomial • 3rd – “Unfoil”

  6. Trinomials continued… • 1st term is a perfect square, last term is a perfect square, middle term is double the product of the square roots of the first and last terms. Then, subtract or add depending on sign of middle term. • Ex: 4x2 – 4x +1  (2x -1)2 Square root of 4x2 is 2x, square root of 1 is 1, 2(2x * 1) = 4x • Ex: 9x2 + 24x + 16  (3x + 4)2 Square root of 9x2 is 3x, square root of 16 is 4, 2(3x * 4) = 24x

  7. Trinomials continued… “Unfoil” • Find the factors of the first and last terms. How can we get the middle term with them? • If it’s a + and + or a – and +, you need to multiply and then add to get the middle term. You will factor as a - - or a + +. • If it’s a + and -, then you need to multiply then subtract to get the middle term. You will factor as a + -.

  8. Examples: • If it’s a + and + or a – and +, you need to multiply and then add to get the middle term. You will factor as a + + or a - -. • a2 + 7a + 6 = (a + 6) (a + 1) • x2 – 5x + 6 = (x – 3) (x – 2)

  9. Examples: • If it’s a + and -, then you need to multiply then subtract to get the middle term. You will factor as a + -. • x2 + 4x – 5 = (x + 5) (x – 1)

  10. What if it’s a polynomial of 4 or more? • 1st – Factor out GCF • 2nd – Factor by Grouping

  11. Factoring by Grouping Ex: x3 + 3x2 + 2x +6 • Group two terms together. (x3 + 3x2) + (2x + 6) 2. Factor out a GCF from each separate binomial to get a common binomial. x2 (x + 3) + 2(x + 3) 3. Factor out the common binomial. (x+3) (x2 + 2)

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