Divide (-2x^3+7x^2+9x)÷(x)

$(- 2 x^{3} + 7 x^{2} + 9 x) \div (x)$

Step 1

Rewrite the division as a fraction.

$\frac{- 2 x^{3} + 7 x^{2} + 9 x}{x}$

Step 2

Simplify the numerator.

Factor $x$ out of $- 2 x^{3} + 7 x^{2} + 9 x$ .

Factor $x$ out of $- 2 x^{3}$ .

$\frac{x (- 2 x^{2}) + 7 x^{2} + 9 x}{x}$

Factor $x$ out of $7 x^{2}$ .

$\frac{x (- 2 x^{2}) + x (7 x) + 9 x}{x}$

Factor $x$ out of $9 x$ .

$\frac{x (- 2 x^{2}) + x (7 x) + x \cdot 9}{x}$

Factor $x$ out of $x (- 2 x^{2}) + x (7 x)$ .

$\frac{x (- 2 x^{2} + 7 x) + x \cdot 9}{x}$

Factor $x$ out of $x (- 2 x^{2} + 7 x) + x \cdot 9$ .

$\frac{x (- 2 x^{2} + 7 x + 9)}{x}$

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 $a \cdot c = - 2 \cdot 9 = - 18$ and whose sum is $b = 7$ .

Factor $7$ out of $7 x$ .

$\frac{x (- 2 x^{2} + 7 (x) + 9)}{x}$

Rewrite $7$ as $- 2$ plus $9$

$\frac{x (- 2 x^{2} + (- 2 + 9) x + 9)}{x}$

Apply the distributive property.

$\frac{x (- 2 x^{2} - 2 x + 9 x + 9)}{x}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{x ((- 2 x^{2} - 2 x) + 9 x + 9)}{x}$

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

$\frac{x (2 x (- x - 1) - 9 (- x - 1))}{x}$

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

$\frac{x ((- x - 1) (2 x - 9))}{x}$

$\frac{x (- x - 1) (2 x - 9)}{x}$

Step 3

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{x (- x - 1) (2 x - 9)}{x}$

Divide $(- x - 1) (2 x - 9)$ by $1$ .

$(- x - 1) (2 x - 9)$

Step 4

Expand $(- x - 1) (2 x - 9)$ using the FOIL Method.

Apply the distributive property.

$- x (2 x - 9) - 1 (2 x - 9)$

Apply the distributive property.

$- x (2 x) - x \cdot - 9 - 1 (2 x - 9)$

Apply the distributive property.

$- x (2 x) - x \cdot - 9 - 1 (2 x) - 1 \cdot - 9$

Step 5

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$- 1 \cdot 2 x \cdot x - x \cdot - 9 - 1 (2 x) - 1 \cdot - 9$

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

Move $x$ .

$- 1 \cdot 2 (x \cdot x) - x \cdot - 9 - 1 (2 x) - 1 \cdot - 9$

Multiply $x$ by $x$ .

$- 1 \cdot 2 x^{2} - x \cdot - 9 - 1 (2 x) - 1 \cdot - 9$

Multiply $- 1$ by $2$ .

$- 2 x^{2} - x \cdot - 9 - 1 (2 x) - 1 \cdot - 9$

Multiply $- 9$ by $- 1$ .

$- 2 x^{2} + 9 x - 1 (2 x) - 1 \cdot - 9$

Multiply $2$ by $- 1$ .

$- 2 x^{2} + 9 x - 2 x - 1 \cdot - 9$

Multiply $- 1$ by $- 9$ .

$- 2 x^{2} + 9 x - 2 x + 9$

Subtract $2 x$ from $9 x$ .

$- 2 x^{2} + 7 x + 9$

Divide (-2x^3+7x^2+9x)÷(x)

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