Factoring Trinomial using AC Method



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

step 2:2x[3x2+(-20)x+28]  Write trinomial in sandard 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 factors 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.
Factor of 84 are:-1,84 -4,-21 -6,-14 -7,-12
Select factor pair such that their sum is b term=-20

step 5:Sprit middle term b order factors as multiple of the a and c terms

step 6:Factor out something common to first two terms.

step 7:Factor out same binominal in last two terms.

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.

by Iwaken

Version 1