Factor 2y^2+11y+5

$2 y^{2} + 11 y + 5$

Step 1

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 $11 y$ .

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

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

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

Apply the distributive property.

$2 y^{2} + 1 y + 10 y + 5$

Multiply $y$ by $1$ .

$2 y^{2} + y + 10 y + 5$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$y (2 y + 1) + 5 (2 y + 1)$

Step 3

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

$(2 y + 1) (y + 5)$

Factor 2y^2+11y+5

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