Algebra Examples

$6 x^{4} - 9 x^{3} - 36 x^{2} + 54 x$

Step 1

Factor $3 x$ out of $6 x^{4} - 9 x^{3} - 36 x^{2} + 54 x$ .

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Step 1.1

Factor $3 x$ out of $6 x^{4}$ .

$3 x (2 x^{3}) - 9 x^{3} - 36 x^{2} + 54 x$

Step 1.2

Factor $3 x$ out of $- 9 x^{3}$ .

$3 x (2 x^{3}) + 3 x (- 3 x^{2}) - 36 x^{2} + 54 x$

Step 1.3

Factor $3 x$ out of $- 36 x^{2}$ .

$3 x (2 x^{3}) + 3 x (- 3 x^{2}) + 3 x (- 12 x) + 54 x$

Step 1.4

Factor $3 x$ out of $54 x$ .

$3 x (2 x^{3}) + 3 x (- 3 x^{2}) + 3 x (- 12 x) + 3 x (18)$

Step 1.5

Factor $3 x$ out of $3 x (2 x^{3}) + 3 x (- 3 x^{2})$ .

$3 x (2 x^{3} - 3 x^{2}) + 3 x (- 12 x) + 3 x (18)$

Step 1.6

Factor $3 x$ out of $3 x (2 x^{3} - 3 x^{2}) + 3 x (- 12 x)$ .

$3 x (2 x^{3} - 3 x^{2} - 12 x) + 3 x (18)$

Step 1.7

Factor $3 x$ out of $3 x (2 x^{3} - 3 x^{2} - 12 x) + 3 x (18)$ .

$3 x (2 x^{3} - 3 x^{2} - 12 x + 18)$

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.

$3 x ((2 x^{3} - 3 x^{2}) - 12 x + 18)$

Step 2.2

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

$3 x (x^{2} (2 x - 3) - 6 (2 x - 3))$

Step 3

Factor.

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Step 3.1

Factor the polynomial by factoring out the greatest common factor, $2 x - 3$ .

$3 x ((2 x - 3) (x^{2} - 6))$

Step 3.2

Remove unnecessary parentheses.

$3 x (2 x - 3) (x^{2} - 6)$