Pre-Algebra Examples

$\frac{30 x^{5} - 36 x^{3} + 15 x^{2}}{6 x^{2}}$

Step 1

Factor $3 x^{2}$ out of $30 x^{5} - 36 x^{3} + 15 x^{2}$ .

Tap for more steps...

Step 1.1

Factor $3 x^{2}$ out of $30 x^{5}$ .

$\frac{3 x^{2} (10 x^{3}) - 36 x^{3} + 15 x^{2}}{6 x^{2}}$

Step 1.2

Factor $3 x^{2}$ out of $- 36 x^{3}$ .

$\frac{3 x^{2} (10 x^{3}) + 3 x^{2} (- 12 x) + 15 x^{2}}{6 x^{2}}$

Step 1.3

Factor $3 x^{2}$ out of $15 x^{2}$ .

$\frac{3 x^{2} (10 x^{3}) + 3 x^{2} (- 12 x) + 3 x^{2} (5)}{6 x^{2}}$

Step 1.4

Factor $3 x^{2}$ out of $3 x^{2} (10 x^{3}) + 3 x^{2} (- 12 x)$ .

$\frac{3 x^{2} (10 x^{3} - 12 x) + 3 x^{2} (5)}{6 x^{2}}$

Step 1.5

Factor $3 x^{2}$ out of $3 x^{2} (10 x^{3} - 12 x) + 3 x^{2} (5)$ .

$\frac{3 x^{2} (10 x^{3} - 12 x + 5)}{6 x^{2}}$

Step 2

Cancel the common factor of $3$ and $6$ .

Tap for more steps...

Step 2.1

Factor $3$ out of $3 x^{2} (10 x^{3} - 12 x + 5)$ .

$\frac{3 (x^{2} (10 x^{3} - 12 x + 5))}{6 x^{2}}$

Step 2.2

Cancel the common factors.

Tap for more steps...

Step 2.2.1

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

$\frac{3 (x^{2} (10 x^{3} - 12 x + 5))}{3 (2 x^{2})}$

Step 2.2.2

Cancel the common factor.

$\frac{3 (x^{2} (10 x^{3} - 12 x + 5))}{3 (2 x^{2})}$

Step 2.2.3

Rewrite the expression.

$\frac{x^{2} (10 x^{3} - 12 x + 5)}{2 x^{2}}$

Step 3

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

Tap for more steps...

Step 3.1

Cancel the common factor.

$\frac{x^{2} (10 x^{3} - 12 x + 5)}{2 x^{2}}$

Step 3.2

Rewrite the expression.

$\frac{10 x^{3} - 12 x + 5}{2}$

Step 4

Split the fraction $\frac{10 x^{3} - 12 x + 5}{2}$ into two fractions.

$\frac{10 x^{3} - 12 x}{2} + \frac{5}{2}$

Step 5

Split the fraction $\frac{10 x^{3} - 12 x}{2}$ into two fractions.

$\frac{10 x^{3}}{2} + \frac{- 12 x}{2} + \frac{5}{2}$

Step 6

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

Tap for more steps...

Step 6.1

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

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

Step 6.2

Cancel the common factors.

Tap for more steps...

Step 6.2.1

Factor $2$ out of $2$ .

$\frac{2 (5 x^{3})}{2 (1)} + \frac{- 12 x}{2} + \frac{5}{2}$

Step 6.2.2

Cancel the common factor.

$\frac{2 (5 x^{3})}{2 \cdot 1} + \frac{- 12 x}{2} + \frac{5}{2}$

Step 6.2.3

Rewrite the expression.

$\frac{5 x^{3}}{1} + \frac{- 12 x}{2} + \frac{5}{2}$

Step 6.2.4

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

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

Step 7

Cancel the common factor of $- 12$ and $2$ .

Tap for more steps...

Step 7.1

Factor $2$ out of $- 12 x$ .

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

Step 7.2

Cancel the common factors.

Tap for more steps...

Step 7.2.1

Factor $2$ out of $2$ .

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

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

Step 7.2.4

Divide $- 6 x$ by $1$ .

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