# Factoring Trinomial using AC Method

### Solve:6x^{3}-40x^{2}+56x

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

step 2:**2x[3x**^{2}+(-20)x+28] Write trinomial in sandard form ax^{2}+bx+c

step 3:**2x[3x**^{2}+(-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

**2x[3x**^{2}+(-6)x+(-14)x+28)]

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

**2x[3x**^{2}+(-6)x+(-14)x+(-28)]→2x[3x(x-2)+(-14)x+28]

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

**2x[3x(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.

#### by Iwaken

Version 1