Divide (3x^3+10x^2+7x)/(x+1)

$\frac{3 x^{3} + 10 x^{2} + 7 x}{x + 1}$

Simplify the numerator.

Factor $x$ out of $3 x^{3} + 10 x^{2} + 7 x$ .

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

$\frac{x (3 x^{2}) + 10 x^{2} + 7 x}{x + 1}$

Factor $x$ out of $10 x^{2}$ .

$\frac{x (3 x^{2}) + x (10 x) + 7 x}{x + 1}$

Factor $x$ out of $7 x$ .

$\frac{x (3 x^{2}) + x (10 x) + x \cdot 7}{x + 1}$

Factor $x$ out of $x (3 x^{2}) + x (10 x)$ .

$\frac{x (3 x^{2} + 10 x) + x \cdot 7}{x + 1}$

Factor $x$ out of $x (3 x^{2} + 10 x) + x \cdot 7$ .

$\frac{x (3 x^{2} + 10 x + 7)}{x + 1}$

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 $a \cdot c = 3 \cdot 7 = 21$ and whose sum is $b = 10$ .

Factor $10$ out of $10 x$ .

$\frac{x (3 x^{2} + 10 (x) + 7)}{x + 1}$

Rewrite $10$ as $3$ plus $7$

$\frac{x (3 x^{2} + (3 + 7) x + 7)}{x + 1}$

Apply the distributive property.

$\frac{x (3 x^{2} + 3 x + 7 x + 7)}{x + 1}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{x ((3 x^{2} + 3 x) + 7 x + 7)}{x + 1}$

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

$\frac{x (3 x (x + 1) + 7 (x + 1))}{x + 1}$

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

$\frac{x ((x + 1) (3 x + 7))}{x + 1}$

$\frac{x (x + 1) (3 x + 7)}{x + 1}$

Cancel the common factor of $x + 1$ .

Cancel the common factor.

$\frac{x (x + 1) (3 x + 7)}{x + 1}$

Divide $x (3 x + 7)$ by $1$ .

$x (3 x + 7)$

Apply the distributive property.

$x (3 x) + x \cdot 7$

Rewrite using the commutative property of multiplication.

$3 x \cdot x + x \cdot 7$

Move $7$ to the left of $x$ .

$3 x \cdot x + 7 \cdot x$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$3 (x \cdot x) + 7 \cdot x$

Multiply $x$ by $x$ .

$3 x^{2} + 7 \cdot x$

$3 x^{2} + 7 x$

Divide (3x^3+10x^2+7x)/(x+1)

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