Answer
$2(4x-7)(x-1)$
Work Step by Step
Factoring by grouping:
1. Multiply the leading coefficient, a, and the constant, c.
2. Find the factors of ac whose sum is b.
3. Rewrite the middle term, bx, as a sum or difference using the factors from step 2.
4. Factor by grouping
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$12x^{2}-33x+21 =...$
Always start by searching for a GCF ... ($GCF=3$).
$=3(4x^{2}-11x+7)=...$
Now, the parentheses:
1. $\quad ac=28 \qquad $
2. $\quad$sum = $-11\quad$... factors: $-7$ and $-4$
3. $\quad (4x^{2}-11x+7) = (4x^{2}-4x)+(-7x+7)$
4. $\quad$... $= 4x(x-1)+(-7)(x-1) = (4x-7)(x-1) $
$...$= $3(4x-7)(x-1)$
