2x [ (3x-14)(x-2) ] → 2x(3x-14)(x-2) This is the answer
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Step 1: 2x [ 3x2 -20 x + 28 ] Factor out anything commonto 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·cis negative, then factors have opposite signs.
If a·c is positive, then factors have same signs. Sign of b determine sign of factors.
Factors of 84 are: -1, -84 -4, -21 -6, -14 -7, -12
Select factors fair 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 [ 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 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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