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 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 muliple 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 [ 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 monomial.
2x [ (3x - 14)(x - 2) ] → 2x(3x -14)(x - 2) This is the answer
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