Algebra Examples

$\frac{8 x^{6} - 10 x^{4} - 12 x^{3}}{- 4 x^{2}}$

Step 1

Factor $2 x^{3}$ out of $8 x^{6} - 10 x^{4} - 12 x^{3}$ .

Tap for more steps...

Step 1.1

Factor $2 x^{3}$ out of $8 x^{6}$ .

$\frac{2 x^{3} (4 x^{3}) - 10 x^{4} - 12 x^{3}}{- 4 x^{2}}$

Step 1.2

Factor $2 x^{3}$ out of $- 10 x^{4}$ .

$\frac{2 x^{3} (4 x^{3}) + 2 x^{3} (- 5 x) - 12 x^{3}}{- 4 x^{2}}$

Step 1.3

Factor $2 x^{3}$ out of $- 12 x^{3}$ .

$\frac{2 x^{3} (4 x^{3}) + 2 x^{3} (- 5 x) + 2 x^{3} (- 6)}{- 4 x^{2}}$

Step 1.4

Factor $2 x^{3}$ out of $2 x^{3} (4 x^{3}) + 2 x^{3} (- 5 x)$ .

$\frac{2 x^{3} (4 x^{3} - 5 x) + 2 x^{3} (- 6)}{- 4 x^{2}}$

Step 1.5

Factor $2 x^{3}$ out of $2 x^{3} (4 x^{3} - 5 x) + 2 x^{3} (- 6)$ .

$\frac{2 x^{3} (4 x^{3} - 5 x - 6)}{- 4 x^{2}}$

Step 2

Cancel the common factor of $2$ and $- 4$ .

Tap for more steps...

Step 2.1

Factor $2$ out of $2 x^{3} (4 x^{3} - 5 x - 6)$ .

$\frac{2 (x^{3} (4 x^{3} - 5 x - 6))}{- 4 x^{2}}$

Step 2.2

Cancel the common factors.

Tap for more steps...

Step 2.2.1

Factor $2$ out of $- 4 x^{2}$ .

$\frac{2 (x^{3} (4 x^{3} - 5 x - 6))}{2 (- 2 x^{2})}$

Step 2.2.2

Cancel the common factor.

$\frac{2 (x^{3} (4 x^{3} - 5 x - 6))}{2 (- 2 x^{2})}$

Step 2.2.3

Rewrite the expression.

$\frac{x^{3} (4 x^{3} - 5 x - 6)}{- 2 x^{2}}$

Step 3

Cancel the common factor of $x^{3}$ and $x^{2}$ .

Tap for more steps...

Step 3.1

Factor $x^{2}$ out of $x^{3} (4 x^{3} - 5 x - 6)$ .

$\frac{x^{2} (x (4 x^{3} - 5 x - 6))}{- 2 x^{2}}$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

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

$\frac{x^{2} (x (4 x^{3} - 5 x - 6))}{x^{2} \cdot - 2}$

Step 3.2.2

Cancel the common factor.

$\frac{x^{2} (x (4 x^{3} - 5 x - 6))}{x^{2} \cdot - 2}$

Step 3.2.3

Rewrite the expression.

$\frac{x (4 x^{3} - 5 x - 6)}{- 2}$

Step 4

Move the negative in front of the fraction.

$- \frac{x (4 x^{3} - 5 x - 6)}{2}$

Step 5

Apply the distributive property.

$- \frac{x (4 x^{3}) + x (- 5 x) + x \cdot - 6}{2}$

Step 6

Simplify.

Tap for more steps...

Step 6.1

Rewrite using the commutative property of multiplication.

$- \frac{4 x \cdot x^{3} + x (- 5 x) + x \cdot - 6}{2}$

Step 6.2

Rewrite using the commutative property of multiplication.

$- \frac{4 x \cdot x^{3} - 5 x \cdot x + x \cdot - 6}{2}$

Step 6.3

Move $- 6$ to the left of $x$ .

$- \frac{4 x \cdot x^{3} - 5 x \cdot x - 6 \cdot x}{2}$

Step 7

Simplify each term.

Tap for more steps...

Step 7.1

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

Tap for more steps...

Step 7.1.1

Move $x^{3}$ .

$- \frac{4 (x^{3} x) - 5 x \cdot x - 6 \cdot x}{2}$

Step 7.1.2

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

Tap for more steps...

Step 7.1.2.1

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

$- \frac{4 (x^{3} x^{1}) - 5 x \cdot x - 6 \cdot x}{2}$

Step 7.1.2.2

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

$- \frac{4 x^{3 + 1} - 5 x \cdot x - 6 \cdot x}{2}$

Step 7.1.3

Add $3$ and $1$ .

$- \frac{4 x^{4} - 5 x \cdot x - 6 \cdot x}{2}$

Step 7.2

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

Tap for more steps...

Step 7.2.1

Move $x$ .

$- \frac{4 x^{4} - 5 (x \cdot x) - 6 \cdot x}{2}$

Step 7.2.2

Multiply $x$ by $x$ .

$- \frac{4 x^{4} - 5 x^{2} - 6 \cdot x}{2}$

$- \frac{4 x^{4} - 5 x^{2} - 6 x}{2}$

Step 8

Split the fraction $\frac{4 x^{4} - 5 x^{2} - 6 x}{2}$ into two fractions.

$- (\frac{4 x^{4} - 5 x^{2}}{2} + \frac{- 6 x}{2})$

Step 9

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

$- (\frac{4 x^{4}}{2} + \frac{- 5 x^{2}}{2} + \frac{- 6 x}{2})$

Step 10

Cancel the common factor of $4$ and $2$ .

Tap for more steps...

Step 10.1

Factor $2$ out of $4 x^{4}$ .

$- (\frac{2 (2 x^{4})}{2} + \frac{- 5 x^{2}}{2} + \frac{- 6 x}{2})$

Step 10.2

Cancel the common factors.

Tap for more steps...

Step 10.2.1

Factor $2$ out of $2$ .

$- (\frac{2 (2 x^{4})}{2 (1)} + \frac{- 5 x^{2}}{2} + \frac{- 6 x}{2})$

Step 10.2.2

Cancel the common factor.

$- (\frac{2 (2 x^{4})}{2 \cdot 1} + \frac{- 5 x^{2}}{2} + \frac{- 6 x}{2})$

Step 10.2.3

Rewrite the expression.

$- (\frac{2 x^{4}}{1} + \frac{- 5 x^{2}}{2} + \frac{- 6 x}{2})$

Step 10.2.4

Divide $2 x^{4}$ by $1$ .

$- (2 x^{4} + \frac{- 5 x^{2}}{2} + \frac{- 6 x}{2})$

Step 11

Move the negative in front of the fraction.

$- (2 x^{4} - \frac{5 x^{2}}{2} + \frac{- 6 x}{2})$

Step 12

Cancel the common factor of $- 6$ and $2$ .

Tap for more steps...

Step 12.1

Factor $2$ out of $- 6 x$ .

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

Step 12.2

Cancel the common factors.

Tap for more steps...

Step 12.2.1

Factor $2$ out of $2$ .

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

Step 12.2.2

Cancel the common factor.

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

Step 12.2.3

Rewrite the expression.

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

Step 12.2.4

Divide $- 3 x$ by $1$ .

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