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Warm up • Factor the Greatest common factor out of the following polynomials • 4x2 + 8x + 16 • 6x2 + 12x 2x2 + 3x Greatest common Factor • Coefficients – numbers before the variables – Look at coefficients and consider largest number that can divide into all of them • Variables – letters that represent more than one possible value – Look for smallest exponent that all terms have in common Factor by taking the GCF • 4x2 + 20x – 16 3x3 + 2x2 + 7x • 3x2 + 6x 7x2 + 35x – 14 Factoring Trinomials Step one – write factors of last term Step two – find the factors that add to get you middle number Step three – write factors you found as binomials 2 X + 8x + 12 Factoring Trinomials Step one – write factors of last term Step two – find the factors that add to get you middle number Step three – write factors you found as binomials 2 X + 8x + 15 Factoring Trinomials Step one – write factors of last term Step two – find the factors that add to get you middle number Step three – write factors you found as binomials 2 X - 4x + 3 Factoring Trinomials Step one – write factors of last term Step two – find the factors that add to get you middle number Step three – write factors you found as binomials 2 X - 5x + 6 Factoring Trinomials Step one – write factors of last term Step two – find the factors that add to get you middle number Step three – write factors you found as binomials 2 X + 2x - 8 Factoring Trinomials Step one – write factors of last term Step two – find the factors that add to get you middle number Step three – write factors you found as binomials 2 X - x - 12 Factor These Trinomials! Factor each trinomial, if possible. The first four do NOT have leading coefficients, the last two DO have leading coefficients. Watch out for signs!! 1) 2 t – 4t – 21 2) x2 + 12x + 32 3) x2 –10x + 24 4) x2 + 3x – 18 Factoring Trinomials Returning to the FOIL method, F O (3x + 2)(x + 4) = I L Factoring Polynomials where the lead coefficient isn’t one • Example • 6x2 + 5x – 4 Factoring polynomials where the lead coefficient isn’t one • 1) multiply first coefficient with the last coefficient • 2) list the factors of that multiplication • 3) Find the factors that add to the middle term • 4) List out 4 terms • 5) factor by grouping • • • • • 1) multiply first coefficient with the last coefficient 2) list the factors of that multiplication 3) Find the factors that add to the middle term 4) List out 4 terms 5) factor by grouping 2x2 + 7x + 3 • • • • • 1) multiply first coefficient with the last coefficient 2) list the factors of that multiplication 3) Find the factors that add to the middle term 4) List out 4 terms 5) factor by grouping 3x2 - 8x + 4 Factoring Polynomials where the lead coefficient isn’t one • Example • 2x2 - 11x + 15 Factoring Polynomials where the lead coefficient isn’t one • Example • 3x2 + 7x - 20 Types of factoring • Greatest common factor • Factoring a trinomial a = 1 • Factoring a trinomial a ≠ 1 Factor the following polynomials *** Always look for a GCF (greatest common factor) first 4x2 + 16x + 12 Factor the following polynomials *** Always look for a GCF (greatest common factor) first 2x2 + 6x + 8 Factor the following polynomials *** Always look for a GCF (greatest common factor) first 4x2 - 20x + 24