Algebra Examples

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

Step 1

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

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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 $x^{3}$ .

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

Step 1.1.2

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

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

Step 1.1.3

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

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

Step 1.2

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

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

Step 2

Factor using the perfect square rule.

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Step 2.1

Rewrite $1$ as $1^{2}$ .

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

Step 2.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$2 x = 2 \cdot x \cdot 1$

Step 2.3

Rewrite the polynomial.

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

Step 2.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 1$ .

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