Factoring Trinomial using AC Method

Solve: 6x3-40x2+56x

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 factors of a.c If a.c is negative, then factors have opposite signs. If a.c is positive, then factors have same signs. Sighn 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 tern]m = -20

Step 5: Split middle tern ba order factors as multiple of the a and cterms
2x [ 3x2 + (-6)x + (-14)x + 28 ]

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

Step 7: Factor out same binomial 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.

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