Algebra Examples

$x^{5} + 5 x^{2} - 4 x^{3} - 20$

Step 1

Reorder terms.

$x^{5} - 4 x^{3} + 5 x^{2} - 20$

Step 2

Factor out the greatest common factor from each group.

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Step 2.1

Group the first two terms and the last two terms.

$(x^{5} - 4 x^{3}) + 5 x^{2} - 20$

Step 2.2

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

$x^{3} (x^{2} - 4) + 5 (x^{2} - 4)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $x^{2} - 4$ .

$(x^{2} - 4) (x^{3} + 5)$

Step 4

Rewrite $4$ as $2^{2}$ .

$(x^{2} - 2^{2}) (x^{3} + 5)$

Step 5

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 $b = 2$ .

$(x + 2) (x - 2) (x^{3} + 5)$