AC Method of factoring ax2 + bx +c

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ax2 + bx + c 2x2 + 11x + 5 ac 2(5) = b =11 ( ) 2x2 + 10x + 1x

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Presentation transcript:

AC Method of factoring ax2 + bx +c E.Q. How is ax2 + bx +c put into factored form?

AC METHOD 3x2 +11x + 10 Looking at your quadratic equation first list a, b and c. a = 3, b = 11, c = 10 2. Multiply a times c. ac = 3 10 = 30 List all the factors of ac. ac = 30 4. Add factors to find sum of “b = 11” 1 30 -1 -30 2 15 -2 -15 3 10 -3 -10 5 6 -5 -6

Original Equation: 3x2 +11x + 10 5. Use the factors to rewrite the middle term of the original equation. Original Equation: 3x2 +11x + 10 Rewrite as: 3x2 +5x +6x +10 Factor by grouping. (3x2 +5x) (+6x +10) 7. Find GCF of each group 3x2 +5x = x(3x + 5) and 6x +10 = 2(3x + 5) Notice both groups in parenthesis are the same!!!

(x+2)(3x+5) 8. Rewrite your groups x(3x + 5) and 2(3x + 5) to get the final answer. (x+2)(3x+5) 9. Check by FOILing.

Factor These Trinomials! 6t2 + 2t - 4 2x2 + 11x + 5