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

Apr 30, 2015

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

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

taking out the common terms:

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

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

making groups of two,

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