Factoring Quadratic Trinomials

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Presentation transcript:

Factoring Quadratic Trinomials 10.5 Factoring Quadratic Trinomials

To factor trinomials, look at the a,b,c numbers ax2+bx+c Remember: To factor trinomials, look at the a,b,c numbers

3. Look for factors of “ac” that added together give you “b” Steps to Follow: 1. Multiply a*c 2. Set up a t-chart 3. Look for factors of “ac” that added together give you “b” 4. Write answer in (x )(x )

x2-x-12 1(-12)=-12 1. Multiply ac 2. Set up t-chart (x+3)(x-4) ac=-12 one + one - Sum=-1 b 1(-12) -11 11 -1(12) -2(6) 4 (x+3)(x-4) 2(-6) -4 -1 3(-4)

Factor x2- 5x + 6 1(6)=6 (x - 2)(x - 3) 1. Multiply ac 2. Set up t-chart ac=6 two - Sum=-5 b -1(-6) -7 -5 -2(-3) (x - 2)(x - 3)

Factor when 1 isn’t the number in front of x2 6x2 + 7x-5 1. Multiply ac 6(-5)=-30 2. Set up t-chart 3. Since you have a coefficient greater than 1, take your factored terms and factor them too. ac=-30 one + one - Sum=7 b -1(30) 29 1(-30) -2(15) 2(-15) -3(10) -29 13 -13 7 (2x - 1)(3x + 5)

Use the discriminate to show a trinomial won’t factor What happens when you can’t find factors????? Use the discriminate to show a trinomial won’t factor -2x2+3x-6 32 - 4(-2)(-6) 9 – 48 -39 No Real Solutions!