Factoring Polynomials

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Presentation transcript:

Factoring Polynomials Wednesday, September 18, 2013 through Friday, September 20, 2013

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? 1st – Factor out GCF 2nd – Difference of Squares 3rd – Sum of Cubes 4th – Difference of Cubes

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)

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

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

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 + -.

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)

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)

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

Factoring by Grouping Ex: x3 + 3x2 + 2x +6 Group two terms together. 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)