Divide (2x^3-3x^2-5x)÷(2x-5)

$(2 x^{3} - 3 x^{2} - 5 x) \div (2 x - 5)$

Step 1

Rewrite the division as a fraction.

$\frac{2 x^{3} - 3 x^{2} - 5 x}{2 x - 5}$

Step 2

Simplify the numerator.

Factor $x$ out of $2 x^{3} - 3 x^{2} - 5 x$ .

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

$\frac{x (2 x^{2}) - 3 x^{2} - 5 x}{2 x - 5}$

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

$\frac{x (2 x^{2}) + x (- 3 x) - 5 x}{2 x - 5}$

Factor $x$ out of $- 5 x$ .

$\frac{x (2 x^{2}) + x (- 3 x) + x \cdot - 5}{2 x - 5}$

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

$\frac{x (2 x^{2} - 3 x) + x \cdot - 5}{2 x - 5}$

Factor $x$ out of $x (2 x^{2} - 3 x) + x \cdot - 5$ .

$\frac{x (2 x^{2} - 3 x - 5)}{2 x - 5}$

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 $b = - 3$ .

Factor $- 3$ out of $- 3 x$ .

$\frac{x (2 x^{2} - 3 (x) - 5)}{2 x - 5}$

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

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$\frac{x (2 x (x + 1) - 5 (x + 1))}{2 x - 5}$

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

$\frac{x ((x + 1) (2 x - 5))}{2 x - 5}$

$\frac{x (x + 1) (2 x - 5)}{2 x - 5}$

Step 3

Cancel the common factor of $2 x - 5$ .

Cancel the common factor.

$\frac{x (x + 1) (2 x - 5)}{2 x - 5}$

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

$x (x + 1)$

Step 4

Apply the distributive property.

$x \cdot x + x \cdot 1$

Step 5

Multiply $x$ by $x$ .

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

Step 6

Multiply $x$ by $1$ .

$x^{2} + x$

Divide (2x^3-3x^2-5x)÷(2x-5)

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