Algebra Examples

$(2 x^{11} - 5 x^{7} - 10 x^{6}) \div 2 x^{3}$

Step 1

Rewrite the division as a fraction.

$\frac{2 x^{11} - 5 x^{7} - 10 x^{6}}{2 x^{3}}$

Step 2

Factor $x^{6}$ out of $2 x^{11} - 5 x^{7} - 10 x^{6}$ .

Tap for more steps...

Step 2.1

Factor $x^{6}$ out of $2 x^{11}$ .

$\frac{x^{6} (2 x^{5}) - 5 x^{7} - 10 x^{6}}{2 x^{3}}$

Step 2.2

Factor $x^{6}$ out of $- 5 x^{7}$ .

$\frac{x^{6} (2 x^{5}) + x^{6} (- 5 x) - 10 x^{6}}{2 x^{3}}$

Step 2.3

Factor $x^{6}$ out of $- 10 x^{6}$ .

$\frac{x^{6} (2 x^{5}) + x^{6} (- 5 x) + x^{6} \cdot - 10}{2 x^{3}}$

Step 2.4

Factor $x^{6}$ out of $x^{6} (2 x^{5}) + x^{6} (- 5 x)$ .

$\frac{x^{6} (2 x^{5} - 5 x) + x^{6} \cdot - 10}{2 x^{3}}$

Step 2.5

Factor $x^{6}$ out of $x^{6} (2 x^{5} - 5 x) + x^{6} \cdot - 10$ .

$\frac{x^{6} (2 x^{5} - 5 x - 10)}{2 x^{3}}$

Step 3

Cancel the common factor of $x^{6}$ and $x^{3}$ .

Tap for more steps...

Step 3.1

Factor $x^{3}$ out of $x^{6} (2 x^{5} - 5 x - 10)$ .

$\frac{x^{3} (x^{3} (2 x^{5} - 5 x - 10))}{2 x^{3}}$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

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

$\frac{x^{3} (x^{3} (2 x^{5} - 5 x - 10))}{x^{3} \cdot 2}$

Step 3.2.2

Cancel the common factor.

$\frac{x^{3} (x^{3} (2 x^{5} - 5 x - 10))}{x^{3} \cdot 2}$

Step 3.2.3

Rewrite the expression.

$\frac{x^{3} (2 x^{5} - 5 x - 10)}{2}$

Step 4

Apply the distributive property.

$\frac{x^{3} (2 x^{5}) + x^{3} (- 5 x) + x^{3} \cdot - 10}{2}$

Step 5

Simplify.

Tap for more steps...

Step 5.1

Rewrite using the commutative property of multiplication.

$\frac{2 x^{3} x^{5} + x^{3} (- 5 x) + x^{3} \cdot - 10}{2}$

Step 5.2

Rewrite using the commutative property of multiplication.

$\frac{2 x^{3} x^{5} - 5 x^{3} x + x^{3} \cdot - 10}{2}$

Step 5.3

Move $- 10$ to the left of $x^{3}$ .

$\frac{2 x^{3} x^{5} - 5 x^{3} x - 10 \cdot x^{3}}{2}$

Step 6

Simplify each term.

Tap for more steps...

Step 6.1

Multiply $x^{3}$ by $x^{5}$ by adding the exponents.

Tap for more steps...

Step 6.1.1

Move $x^{5}$ .

$\frac{2 (x^{5} x^{3}) - 5 x^{3} x - 10 \cdot x^{3}}{2}$

Step 6.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2 x^{5 + 3} - 5 x^{3} x - 10 \cdot x^{3}}{2}$

Step 6.1.3

Add $5$ and $3$ .

$\frac{2 x^{8} - 5 x^{3} x - 10 \cdot x^{3}}{2}$

Step 6.2

Multiply $x^{3}$ by $x$ by adding the exponents.

Tap for more steps...

Step 6.2.1

Move $x$ .

$\frac{2 x^{8} - 5 (x \cdot x^{3}) - 10 \cdot x^{3}}{2}$

Step 6.2.2

Multiply $x$ by $x^{3}$ .

Tap for more steps...

Step 6.2.2.1

Raise $x$ to the power of $1$ .

$\frac{2 x^{8} - 5 (x^{1} x^{3}) - 10 \cdot x^{3}}{2}$

Step 6.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2 x^{8} - 5 x^{1 + 3} - 10 \cdot x^{3}}{2}$

Step 6.2.3

Add $1$ and $3$ .

$\frac{2 x^{8} - 5 x^{4} - 10 \cdot x^{3}}{2}$

$\frac{2 x^{8} - 5 x^{4} - 10 x^{3}}{2}$

Step 7

Split the fraction $\frac{2 x^{8} - 5 x^{4} - 10 x^{3}}{2}$ into two fractions.

$\frac{2 x^{8} - 5 x^{4}}{2} + \frac{- 10 x^{3}}{2}$

Step 8

Split the fraction $\frac{2 x^{8} - 5 x^{4}}{2}$ into two fractions.

$\frac{2 x^{8}}{2} + \frac{- 5 x^{4}}{2} + \frac{- 10 x^{3}}{2}$

Step 9

Cancel the common factor of $2$ .

Tap for more steps...

Step 9.1

Cancel the common factor.

$\frac{2 x^{8}}{2} + \frac{- 5 x^{4}}{2} + \frac{- 10 x^{3}}{2}$

Step 9.2

Divide $x^{8}$ by $1$ .

$x^{8} + \frac{- 5 x^{4}}{2} + \frac{- 10 x^{3}}{2}$

Step 10

Move the negative in front of the fraction.

$x^{8} - \frac{5 x^{4}}{2} + \frac{- 10 x^{3}}{2}$

Step 11

Cancel the common factor of $- 10$ and $2$ .

Tap for more steps...

Step 11.1

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

$x^{8} - \frac{5 x^{4}}{2} + \frac{2 (- 5 x^{3})}{2}$

Step 11.2

Cancel the common factors.

Tap for more steps...

Step 11.2.1

Factor $2$ out of $2$ .

$x^{8} - \frac{5 x^{4}}{2} + \frac{2 (- 5 x^{3})}{2 (1)}$

Step 11.2.2

Cancel the common factor.

$x^{8} - \frac{5 x^{4}}{2} + \frac{2 (- 5 x^{3})}{2 \cdot 1}$

Step 11.2.3

Rewrite the expression.

$x^{8} - \frac{5 x^{4}}{2} + \frac{- 5 x^{3}}{1}$

Step 11.2.4

Divide $- 5 x^{3}$ by $1$ .

$x^{8} - \frac{5 x^{4}}{2} - 5 x^{3}$