# How do you factor by grouping 6x^3 - 2x + 3x^2 - 1?

Apr 30, 2015

we are given, 6${x}^{3}$ $-$ 2$x$ $+$3${x}^{2}$ $-$ 1

on rearrangement:

$=$ 6${x}^{3}$ $+$ 3${x}^{2}$ $-$ 2$x$ $-$ 1

The first two terms have 3${x}^{2}$ in common and the last two terms have $-$1 in common:

taking out the common terms:

$=$ 3${x}^{2}$ ( $2 x$ + 1) $-$ 1 ( 2$x$ $+$ 1)

making groups of two:
$=$ (3 ${x}^{2}$ $-$1) ( $2 x$ $+$ 1 )