Pre-Algebra Examples

$(49 x^{5} - 14 x^{3} + 8 x^{2}) \div 7 x^{2}$

Step 1

Rewrite the division as a fraction.

$\frac{49 x^{5} - 14 x^{3} + 8 x^{2}}{7 x^{2}}$

Step 2

Factor $x^{2}$ out of $49 x^{5} - 14 x^{3} + 8 x^{2}$ .

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Step 2.1

Factor $x^{2}$ out of $49 x^{5}$ .

$\frac{x^{2} (49 x^{3}) - 14 x^{3} + 8 x^{2}}{7 x^{2}}$

Step 2.2

Factor $x^{2}$ out of $- 14 x^{3}$ .

$\frac{x^{2} (49 x^{3}) + x^{2} (- 14 x) + 8 x^{2}}{7 x^{2}}$

Step 2.3

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

$\frac{x^{2} (49 x^{3}) + x^{2} (- 14 x) + x^{2} \cdot 8}{7 x^{2}}$

Step 2.4

Factor $x^{2}$ out of $x^{2} (49 x^{3}) + x^{2} (- 14 x)$ .

$\frac{x^{2} (49 x^{3} - 14 x) + x^{2} \cdot 8}{7 x^{2}}$

Step 2.5

Factor $x^{2}$ out of $x^{2} (49 x^{3} - 14 x) + x^{2} \cdot 8$ .

$\frac{x^{2} (49 x^{3} - 14 x + 8)}{7 x^{2}}$

Step 3

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

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Step 3.1

Cancel the common factor.

$\frac{x^{2} (49 x^{3} - 14 x + 8)}{7 x^{2}}$

Step 3.2

Rewrite the expression.

$\frac{49 x^{3} - 14 x + 8}{7}$

Step 4

Split the fraction $\frac{49 x^{3} - 14 x + 8}{7}$ into two fractions.

$\frac{49 x^{3} - 14 x}{7} + \frac{8}{7}$

Step 5

Split the fraction $\frac{49 x^{3} - 14 x}{7}$ into two fractions.

$\frac{49 x^{3}}{7} + \frac{- 14 x}{7} + \frac{8}{7}$

Step 6

Cancel the common factor of $49$ and $7$ .

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Step 6.1

Factor $7$ out of $49 x^{3}$ .

$\frac{7 (7 x^{3})}{7} + \frac{- 14 x}{7} + \frac{8}{7}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $7$ out of $7$ .

$\frac{7 (7 x^{3})}{7 (1)} + \frac{- 14 x}{7} + \frac{8}{7}$

Step 6.2.2

Cancel the common factor.

$\frac{7 (7 x^{3})}{7 \cdot 1} + \frac{- 14 x}{7} + \frac{8}{7}$

Step 6.2.3

Rewrite the expression.

$\frac{7 x^{3}}{1} + \frac{- 14 x}{7} + \frac{8}{7}$

Step 6.2.4

Divide $7 x^{3}$ by $1$ .

$7 x^{3} + \frac{- 14 x}{7} + \frac{8}{7}$

Step 7

Cancel the common factor of $- 14$ and $7$ .

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Step 7.1

Factor $7$ out of $- 14 x$ .

$7 x^{3} + \frac{7 (- 2 x)}{7} + \frac{8}{7}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $7$ out of $7$ .

$7 x^{3} + \frac{7 (- 2 x)}{7 (1)} + \frac{8}{7}$

Step 7.2.2

Cancel the common factor.

$7 x^{3} + \frac{7 (- 2 x)}{7 \cdot 1} + \frac{8}{7}$

Step 7.2.3

Rewrite the expression.

$7 x^{3} + \frac{- 2 x}{1} + \frac{8}{7}$

Step 7.2.4

Divide $- 2 x$ by $1$ .

$7 x^{3} - 2 x + \frac{8}{7}$