Address the potential confusion head-on for the sign of the quantity that you are factoring out in the second pair.
Then, there should be no doubts:
x3−3x2−x+3 =
x2(x−3)−x+3
For this expression to factor, there
must be an (x - 3) factor in the second pair, so deliberately write it there,
with a few spaces in front of it for a plus sign or subtraction sign (depending), and a constant for a placeholder.
x2(x−3) (x−3)
What multiplied by x equals -x? Negative one does. Write this in as a subtraction sign and 1 next to the second
(x - 3) factor.
x2(x−3)−1(x−3)
Lastly, check to see if (-1) multiplied by the (-3) of (x - 3) gives 3, the last term of the original polynomial expression.
It does.
Factor out the common factor of (x - 3), either to the right, or to the left, of
(x2−1).
Then,
(x2−1)(x−3) =
(x−1)(x+1)(x−3)
It just took me a lot of words and some minutes of hen-and-peck typing to explain this, but a newer student could
casually write out the steps on paper to fully factoring this by the grouping method in about 20 seconds, give or
take some seconds.
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This could also been factored by grouping this way, with keeping the highest degree term first:
x3−3x3−x+3 =
x3−x−3x2+3 =
x(x2−1) − 3(x2−1) =
(x2−1)(x−3) =
(x−1)(x+1)(x−3)