Divide (x^2+5xy+6y^2)/(x+2y)

$\frac{x^{2} + 5 x y + 6 y^{2}}{x + 2 y}$

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 $a \cdot c = 1 \cdot 6 = 6$ and whose sum is $b = 5$ .

Reorder terms.

$\frac{x^{2} + 6 y^{2} + 5 x y}{x + 2 y}$

Reorder $6 y^{2}$ and $5 x y$ .

$\frac{x^{2} + 5 x y + 6 y^{2}}{x + 2 y}$

Factor $5$ out of $5 x y$ .

$\frac{x^{2} + 5 (x y) + 6 y^{2}}{x + 2 y}$

Rewrite $5$ as $2$ plus $3$

$\frac{x^{2} + (2 + 3) (x y) + 6 y^{2}}{x + 2 y}$

Apply the distributive property.

$\frac{x^{2} + 2 (x y) + 3 (x y) + 6 y^{2}}{x + 2 y}$

Move parentheses.

$\frac{x^{2} + 2 x y + 3 x y + 6 y^{2}}{x + 2 y}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(x^{2} + 2 x y) + 3 x y + 6 y^{2}}{x + 2 y}$

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

$\frac{x (x + 2 y) + 3 y (x + 2 y)}{x + 2 y}$

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

$\frac{(x + 2 y) (x + 3 y)}{x + 2 y}$

Cancel the common factor of $x + 2 y$ .

Cancel the common factor.

$\frac{(x + 2 y) (x + 3 y)}{x + 2 y}$

Divide $x + 3 y$ by $1$ .

$x + 3 y$

Divide (x^2+5xy+6y^2)/(x+2y)

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