Calculus Examples

$8 x^{5} + 4 x^{4} + 4 x^{3} + 2 x^{2}$

Step 1

Factor $2 x^{2}$ out of $8 x^{5} + 4 x^{4} + 4 x^{3} + 2 x^{2}$ .

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Step 1.1

Factor $2 x^{2}$ out of $8 x^{5}$ .

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

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

$2 x^{2} (4 x^{3}) + 2 x^{2} (2 x^{2}) + 2 x^{2} (2 x) + 2 x^{2} (1)$

Step 1.5

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

$2 x^{2} (4 x^{3} + 2 x^{2}) + 2 x^{2} (2 x) + 2 x^{2} (1)$

Step 1.6

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

$2 x^{2} (4 x^{3} + 2 x^{2} + 2 x) + 2 x^{2} (1)$

Step 1.7

Factor $2 x^{2}$ out of $2 x^{2} (4 x^{3} + 2 x^{2} + 2 x) + 2 x^{2} (1)$ .

$2 x^{2} (4 x^{3} + 2 x^{2} + 2 x + 1)$

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.

$2 x^{2} ((4 x^{3} + 2 x^{2}) + 2 x + 1)$

Step 2.2

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

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

Step 3

Factor.

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Step 3.1

Factor the polynomial by factoring out the greatest common factor, $2 x + 1$ .

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

Step 3.2

Remove unnecessary parentheses.

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