Finite Math Examples

$x^{4} - 3 x^{3} + 5 x^{2} - 15 x$

Step 1

Factor out the GCF of $x$ from $x^{4} - 3 x^{3} + 5 x^{2} - 15 x$ .

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Step 1.1

Factor out the GCF of $x$ from each term in the polynomial.

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Step 1.1.1

Factor out the GCF of $x$ from the expression $x^{4}$ .

$x (x^{3}) - 3 x^{3} + 5 x^{2} - 15 x$

Step 1.1.2

Factor out the GCF of $x$ from the expression $- 3 x^{3}$ .

$x (x^{3}) + x (- 3 x^{2}) + 5 x^{2} - 15 x$

Step 1.1.3

Factor out the GCF of $x$ from the expression $5 x^{2}$ .

$x (x^{3}) + x (- 3 x^{2}) + x (5 x) - 15 x$

Step 1.1.4

Factor out the GCF of $x$ from the expression $- 15 x$ .

$x (x^{3}) + x (- 3 x^{2}) + x (5 x) + x (- 15)$

Step 1.2

Since all the terms share a common factor of $x$ , it can be factored out of each term.

$x (x^{3} - 3 x^{2} + 5 x - 15)$

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.

$x ((x^{3} - 3 x^{2}) + 5 x - 15)$

Step 2.2

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

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

Step 3

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

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