Factor 4x^2+22x+10

$4 x^{2} + 22 x + 10$

Step 1

Factor $2$ out of $4 x^{2} + 22 x + 10$ .

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

$2 (2 x^{2}) + 22 x + 10$

Factor $2$ out of $22 x$ .

$2 (2 x^{2}) + 2 (11 x) + 10$

Factor $2$ out of $10$ .

$2 (2 x^{2}) + 2 (11 x) + 2 (5)$

Factor $2$ out of $2 (2 x^{2}) + 2 (11 x)$ .

$2 (2 x^{2} + 11 x) + 2 (5)$

Factor $2$ out of $2 (2 x^{2} + 11 x) + 2 (5)$ .

$2 (2 x^{2} + 11 x + 5)$

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 $a \cdot c = 2 \cdot 5 = 10$ and whose sum is $b = 11$ .

Factor $11$ out of $11 x$ .

$2 (2 x^{2} + 11 (x) + 5)$

Rewrite $11$ as $1$ plus $10$

$2 (2 x^{2} + (1 + 10) x + 5)$

Apply the distributive property.

$2 (2 x^{2} + 1 x + 10 x + 5)$

Multiply $x$ by $1$ .

$2 (2 x^{2} + x + 10 x + 5)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$2 ((2 x^{2} + x) + 10 x + 5)$

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

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

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

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

Remove unnecessary parentheses.

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

Factor 4x^2+22x+10

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