Pre-Algebra Examples

$3 x^{3} - 2 x^{2} - 3 x + 2$

Step 1

Factor out the greatest common factor from each group.

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Step 1.1

Group the first two terms and the last two terms.

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

Step 1.2

Factor out the greatest common factor (GCF) from each group.

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

Step 2

Factor the polynomial by factoring out the greatest common factor,

$3 x - 2$ .

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

Step 3

Rewrite

$1$ as

$1^{2}$ .

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

Step 4

Factor.

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Step 4.1

Since both terms are perfect squares, factor using the difference of squares formula,

$a^{2} - b^{2} = (a + b) (a - b)$ where

$a = x$ and

$b = 1$ .

$(3 x - 2) ((x + 1) (x - 1))$

Step 4.2

Remove unnecessary parentheses.

$(3 x - 2) (x + 1) (x - 1)$