Pre-Algebra Examples

$(30 x^{5} + 35^{4} - 90^{3}) \div 5 x^{2}$

Step 1

Rewrite the division as a fraction.

$\frac{30 x^{5} + 35^{4} - 90^{3}}{5 x^{2}}$

Step 2

Simplify the numerator.

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Step 2.1

Raise $35$ to the power of $4$ .

$\frac{30 x^{5} + 1500625 - 90^{3}}{5 x^{2}}$

Step 2.2

Raise $90$ to the power of $3$ .

$\frac{30 x^{5} + 1500625 - 1 \cdot 729000}{5 x^{2}}$

Step 2.3

Multiply $- 1$ by $729000$ .

$\frac{30 x^{5} + 1500625 - 729000}{5 x^{2}}$

Step 2.4

Subtract $729000$ from $1500625$ .

$\frac{30 x^{5} + 771625}{5 x^{2}}$

Step 2.5

Factor $5$ out of $30 x^{5} + 771625$ .

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Step 2.5.1

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

$\frac{5 (6 x^{5}) + 771625}{5 x^{2}}$

Step 2.5.2

Factor $5$ out of $771625$ .

$\frac{5 (6 x^{5}) + 5 (154325)}{5 x^{2}}$

Step 2.5.3

Factor $5$ out of $5 (6 x^{5}) + 5 (154325)$ .

$\frac{5 (6 x^{5} + 154325)}{5 x^{2}}$

Step 3

Cancel the common factor of $5$ .

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Step 3.1

Cancel the common factor.

$\frac{5 (6 x^{5} + 154325)}{5 x^{2}}$

Step 3.2

Rewrite the expression.

$\frac{6 x^{5} + 154325}{x^{2}}$

Step 4

Split the fraction $\frac{6 x^{5} + 154325}{x^{2}}$ into two fractions.

$\frac{6 x^{5}}{x^{2}} + \frac{154325}{x^{2}}$

Step 5

Cancel the common factor of $x^{5}$ and $x^{2}$ .

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Step 5.1

Factor $x^{2}$ out of $6 x^{5}$ .

$\frac{x^{2} (6 x^{3})}{x^{2}} + \frac{154325}{x^{2}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Multiply by $1$ .

$\frac{x^{2} (6 x^{3})}{x^{2} \cdot 1} + \frac{154325}{x^{2}}$

Step 5.2.2

Cancel the common factor.

$\frac{x^{2} (6 x^{3})}{x^{2} \cdot 1} + \frac{154325}{x^{2}}$

Step 5.2.3

Rewrite the expression.

$\frac{6 x^{3}}{1} + \frac{154325}{x^{2}}$

Step 5.2.4

Divide $6 x^{3}$ by $1$ .

$6 x^{3} + \frac{154325}{x^{2}}$