Answer
$(x-5)(3x-2)$
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. $\quad ac=+30$
2. $\quad$sum = $-17 \quad$... factors: $-15$ and $-2$
3. $\quad 3x^{2}-17x+10=(3x^{2}-15x)+(-2x+10)$
4. $\quad$... $=3x(x-5) +(-2)(x-5) =(x-5)(3x-2)$
Check by FOIL
$F:\quad 3x^{2}$
$O:\quad -2x$
$I:\quad -15x$
$L:\quad +10$
$(x-5)(3x-2)$ = $3x^{2}-17x+10$
