Answer
$(3x-2)(5x-3)$
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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$15x^{2}-19x+6 =...$
Always start by searching for a GCF ... (there are none other than 1).
1. $\quad ac=+90 $
2. $\quad$sum = $-19\quad$... factors: $-10$ and $-9$
3. $\quad$ $15x^{2}-19x+6 = (15x^{2}-10x)+(-9x+6 )$
4. $\quad$... $= 5x(3x-2)+(-3)(3x-2) =(3x-2)(5x-3)$
Check by FOIL
$F:\quad 15x^{2}$
$O:\quad -9x$
$I:\quad -10x$
$L:\quad +6$
$(3x-2)(5x-3)$ = $15x^{2}-19x+6$
