Factoring Trinomial Using AC Method

by Jesus A Acosta

Solve: 6x3 - 40x2 + 56x

Step 1: 2x [ 3x2 - 20x + 28 ]         Factor out anything common to all terms.

Step 2: 2x [ 3x2 + (-20)x + 28 ]         Write trinomial in standard form ax2 + bx + c

Step 3: 2x [ 3x2 + (-20)x + 28 ]         Determine product of a·c = 3·28 = 84

Step 4: List all pairs of a·c If a·c is negative, then factors have opposite signs.
If a·c is positive, then factors have same signs. Sign of b determines sign of factors.
Factors of 84 are: -1, -84     -4, -21     -6, -14     -7, -12
Select factor pair such that their sum is b term = -20

Step 5: Split middle term b order factors as multiple of the a and c terms
2x [3x2 + (-6)x + (-14)x + 28 ]

Step 6: Factor out something common to first two terms.
2x [ 3x2 + (-6)x + (-14)x + 28 ] → 2x [ 3 x(x-2) + (-14)x + 28 ]

Step 7: Factor out same binomial in last two terms.
2x [ 3 x(x-2) + (-14)(x-2) ]

Step 8: Apply Distributive Law and convert trinomial into the product of two binomials and a monomial.
2x [ (3x - 14)(x - 2) ] → 2x(3x - 14)(x - 2) This is the answer Home Button