Answer
$(3x-1)(x+5)$
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. $ac=-15$
2. sum = $+14$ ... factors: $-1$ and $+15$
3.
$3x^{2}+14x-5=(3x^{2}+15x)+(-x-5)$
4.
... $=3x(x+5)+(-1)(x+5)$
$=(3x-1)(x+5)$
Check by FOIL$\qquad (3x-1)(x+5) $=
$F:\quad 3x^{2}$
$O:\quad +15x$
$I:\quad -x$
$L:\quad -5$
$(3x-1)(x+5)$ = $3x^{2}+14x-5$
