Answer
$(2w-3)(3w-4) $
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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Always start by searching for a GCF ... (there are none other than 1).
1. $\quad ac=+72$
2. $\quad$sum = $-17 \quad$... factors: $-8$ and $-9$
3. $\quad$ $6w^{2}-17w+12=(6w^{2}-9w)+(-8w+12)$
4. $\quad$... $=3w(2w-3) +(-4)(2w-3) =(2w-3)(3w-4)$
Check by FOIL
$F:\quad 6w^{2}$
$O:\quad -8w$
$I:\quad -9w$
$L:\quad +12$
$(2w-3)(3w-4) $ = $6w^{2}-17w+12$
