Answer
$(x-3)(5x-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.... none (other than 1).
1. $ac=30$
2. sum = $-17$ ... factors: $-15$ and $-2$
3.
$5x^{2}-17x+6=(5x^{2}-15x)+(-2x+6)$
4.
... $=5x(x-3)+(-2)( x-3)$
$=(x-3)(5x-2)$
Check by FOIL$\qquad (x-3)(5x-2) $=
$F:\quad 5x^{2}$
$O:\quad -2x$
$I:\quad -15x$
$L:\quad +6$
$(x-3)(5x-2) $= $5x^{2}-17x+6$
