The AC Method: Factoring Trinomials of the Form Ax2 + Bx + C - Edubirdie

University:
Campbell University
Course:
MATH 111 | College Algebra
Academic year:

2022
Views:

493

Pages:

1
Author:

trescandogss

The AC Method Factoring Trinomials of the Form Ax2 + Bx + C Set-up steps: Remove all ( ) and combine like terms Make squared term (first term) positive Put in standard quadratic form: Ax2 + Bx + C Factor out a GCF if possible Step 1 Find A•C (Ax2 + Bx + C) Step 2 Find 2 factors of the product A•C whose algebraic sum is B. Same sign binomials--correct factors must ADD to B Different signs--correct factors must have a DIFFERENCE of B Step 3 Re-write middle term as the algebraic sum of the two correct factors Step 4 Factor by grouping (we now have four terms) Example: Factor 12x2 + 25x + 12 by the A•C Method (need two factors of 144 that add to 25) A•C = 144 FACTORS: 12x2 + 25x + 12 12x2 + 9x + 16x + 12 12x2 + 9x +16x + 12 3x(4x + 3) +4(4x + 3) (4x + 3)(3x + 4) NOTE: If there is no pair of factors for A•C that works, then the trinomial does NOT factor.

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