Algebra Examples

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

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.

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

Step 1.2

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

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

Step 2

Factor the polynomial by factoring out the greatest common factor, $x - 2$ .

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

Step 3

Multiply the constant in the polynomial $x^{2} + 1$ by $- i^{2}$ where $i^{2}$ is equal to $- 1$ .

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

Step 4

Factor.

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Step 4.1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - i^{2} = (a + i) (a - i)$ where $a = x$ and $i = i$ .

$(x - 2) ((x + i) (x - i))$

Step 4.2

Remove unnecessary parentheses.

$(x - 2) (x + i) (x - i)$