Factor 20x^3+13x^2+2x

$20 x^{3} + 13 x^{2} + 2 x$

Step 1

Factor $x$ out of $20 x^{3} + 13 x^{2} + 2 x$ .

Factor $x$ out of $20 x^{3}$ .

$x (20 x^{2}) + 13 x^{2} + 2 x$

Factor $x$ out of $13 x^{2}$ .

$x (20 x^{2}) + x (13 x) + 2 x$

Factor $x$ out of $2 x$ .

$x (20 x^{2}) + x (13 x) + x \cdot 2$

Factor $x$ out of $x (20 x^{2}) + x (13 x)$ .

$x (20 x^{2} + 13 x) + x \cdot 2$

Factor $x$ out of $x (20 x^{2} + 13 x) + x \cdot 2$ .

$x (20 x^{2} + 13 x + 2)$

Step 2

Factor.

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 20 \cdot 2 = 40$ and whose sum is $b = 13$ .

Factor $13$ out of $13 x$ .

$x (20 x^{2} + 13 (x) + 2)$

Rewrite $13$ as $5$ plus $8$

$x (20 x^{2} + (5 + 8) x + 2)$

Apply the distributive property.

$x (20 x^{2} + 5 x + 8 x + 2)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$x ((20 x^{2} + 5 x) + 8 x + 2)$

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

$x (5 x (4 x + 1) + 2 (4 x + 1))$

Factor the polynomial by factoring out the greatest common factor, $4 x + 1$ .

$x ((4 x + 1) (5 x + 2))$

Remove unnecessary parentheses.

$x (4 x + 1) (5 x + 2)$

Factor 20x^3+13x^2+2x

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