Finite Math Examples

$2 x^{5} - 6 x^{4} + x^{3} - 3 x^{2} + 3 x - 9$

Step 1

Regroup terms.

$2 x^{5} - 6 x^{4} + x^{3} - 3 x^{2} + 3 x - 9$

Step 2

Factor $2 x^{4}$ out of $2 x^{5} - 6 x^{4}$ .

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Step 2.1

Factor $2 x^{4}$ out of $2 x^{5}$ .

$2 x^{4} (x) - 6 x^{4} + x^{3} - 3 x^{2} + 3 x - 9$

Step 2.2

Factor $2 x^{4}$ out of $- 6 x^{4}$ .

$2 x^{4} (x) + 2 x^{4} (- 3) + x^{3} - 3 x^{2} + 3 x - 9$

Step 2.3

Factor $2 x^{4}$ out of $2 x^{4} (x) + 2 x^{4} (- 3)$ .

$2 x^{4} (x - 3) + x^{3} - 3 x^{2} + 3 x - 9$

Step 3

Factor out the greatest common factor from each group.

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Step 3.1

Group the first two terms and the last two terms.

$2 x^{4} (x - 3) + (x^{3} - 3 x^{2}) + 3 x - 9$

Step 3.2

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

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

Step 4

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

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

Step 5

Factor $x - 3$ out of $2 x^{4} (x - 3) + (x - 3) (x^{2} + 3)$ .

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Step 5.1

Factor $x - 3$ out of $2 x^{4} (x - 3)$ .

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

Step 5.2

Factor $x - 3$ out of $(x - 3) (2 x^{4}) + (x - 3) (x^{2} + 3)$ .

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