Finite Math Examples

$\frac{27 x^{7} - 15 x^{5} - 3 x^{4}}{3 x^{2}}$

Step 1

Factor $3 x^{4}$ out of $27 x^{7} - 15 x^{5} - 3 x^{4}$ .

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Step 1.1

Factor $3 x^{4}$ out of $27 x^{7}$ .

$\frac{3 x^{4} (9 x^{3}) - 15 x^{5} - 3 x^{4}}{3 x^{2}}$

Step 1.2

Factor $3 x^{4}$ out of $- 15 x^{5}$ .

$\frac{3 x^{4} (9 x^{3}) + 3 x^{4} (- 5 x) - 3 x^{4}}{3 x^{2}}$

Step 1.3

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

$\frac{3 x^{4} (9 x^{3}) + 3 x^{4} (- 5 x) + 3 x^{4} (- 1)}{3 x^{2}}$

Step 1.4

Factor $3 x^{4}$ out of $3 x^{4} (9 x^{3}) + 3 x^{4} (- 5 x)$ .

$\frac{3 x^{4} (9 x^{3} - 5 x) + 3 x^{4} (- 1)}{3 x^{2}}$

Step 1.5

Factor $3 x^{4}$ out of $3 x^{4} (9 x^{3} - 5 x) + 3 x^{4} (- 1)$ .

$\frac{3 x^{4} (9 x^{3} - 5 x - 1)}{3 x^{2}}$

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Cancel the common factor.

$\frac{3 x^{4} (9 x^{3} - 5 x - 1)}{3 x^{2}}$

Step 2.2

Rewrite the expression.

$\frac{x^{4} (9 x^{3} - 5 x - 1)}{x^{2}}$

Step 3

Cancel the common factor of $x^{4}$ and $x^{2}$ .

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Step 3.1

Factor $x^{2}$ out of $x^{4} (9 x^{3} - 5 x - 1)$ .

$\frac{x^{2} (x^{2} (9 x^{3} - 5 x - 1))}{x^{2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

$\frac{x^{2} (x^{2} (9 x^{3} - 5 x - 1))}{x^{2} \cdot 1}$

Step 3.2.2

Cancel the common factor.

$\frac{x^{2} (x^{2} (9 x^{3} - 5 x - 1))}{x^{2} \cdot 1}$

Step 3.2.3

Rewrite the expression.

$\frac{x^{2} (9 x^{3} - 5 x - 1)}{1}$

Step 3.2.4

Divide $x^{2} (9 x^{3} - 5 x - 1)$ by $1$ .

$x^{2} (9 x^{3} - 5 x - 1)$

Step 4

Apply the distributive property.

$x^{2} (9 x^{3}) + x^{2} (- 5 x) + x^{2} \cdot - 1$

Step 5

Simplify.

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Step 5.1

Rewrite using the commutative property of multiplication.

$9 x^{2} x^{3} + x^{2} (- 5 x) + x^{2} \cdot - 1$

Step 5.2

Rewrite using the commutative property of multiplication.

$9 x^{2} x^{3} - 5 x^{2} x + x^{2} \cdot - 1$

Step 5.3

Move $- 1$ to the left of $x^{2}$ .

$9 x^{2} x^{3} - 5 x^{2} x - 1 \cdot x^{2}$

Step 6

Simplify each term.

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Step 6.1

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

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Step 6.1.1

Move $x^{3}$ .

$9 (x^{3} x^{2}) - 5 x^{2} x - 1 \cdot x^{2}$

Step 6.1.2

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

$9 x^{3 + 2} - 5 x^{2} x - 1 \cdot x^{2}$

Step 6.1.3

Add $3$ and $2$ .

$9 x^{5} - 5 x^{2} x - 1 \cdot x^{2}$

Step 6.2

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 6.2.1

Move $x$ .

$9 x^{5} - 5 (x \cdot x^{2}) - 1 \cdot x^{2}$

Step 6.2.2

Multiply $x$ by $x^{2}$ .

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Step 6.2.2.1

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

$9 x^{5} - 5 (x^{1} x^{2}) - 1 \cdot x^{2}$

Step 6.2.2.2

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

$9 x^{5} - 5 x^{1 + 2} - 1 \cdot x^{2}$

Step 6.2.3

Add $1$ and $2$ .

$9 x^{5} - 5 x^{3} - 1 \cdot x^{2}$

Step 6.3

Rewrite $- 1 x^{2}$ as $- x^{2}$ .

$9 x^{5} - 5 x^{3} - x^{2}$