Answer
$(3x-1)(x-7)$
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. $ac=+21$
2. sum = $-22$ ... factors: $-1$ and $-21$
3.
$3x^{2}-22x+7=(3x^{2}-21x)+(-x+7)$
4.
... $=3x(x-7)+(-1)(x-7)$
$=(3x-1)(x-7)$
Check by FOIL$\qquad (3x-1)(x-7) $=
$F:\quad 3x^{2}$
$O:\quad -21x$
$I:\quad -x$
$L:\quad +7$
$(3x-1)(x-7)$ = $3x^{2}-22x+7$
