Pre-Algebra Examples

$6 x^{3} + 5 x^{2} - 12 x - 10 \div 6 x + 5$

Step 1

Write $6 x^{3} + 5 x^{2} - 12 x - 10 \div 6 x + 5$ as an equation.

$y = 6 x^{3} + 5 x^{2} - 12 x - 10 \div 6 x + 5$

Step 2

Simplify each term.

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Step 2.1

Rewrite the division as a fraction.

$y = 6 x^{3} + 5 x^{2} - 12 x - \frac{10}{6} x + 5$

Step 2.2

Cancel the common factor of $10$ and $6$ .

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Step 2.2.1

Factor $2$ out of $10$ .

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

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $2$ out of $6$ .

$y = 6 x^{3} + 5 x^{2} - 12 x - \frac{2 \cdot 5}{2 \cdot 3} x + 5$

Step 2.2.2.2

Cancel the common factor.

$y = 6 x^{3} + 5 x^{2} - 12 x - \frac{2 \cdot 5}{2 \cdot 3} x + 5$

Step 2.2.2.3

Rewrite the expression.

$y = 6 x^{3} + 5 x^{2} - 12 x - \frac{5}{3} x + 5$

Step 2.3

Combine $x$ and $\frac{5}{3}$ .

$y = 6 x^{3} + 5 x^{2} - 12 x - \frac{x \cdot 5}{3} + 5$

Step 2.4

Move $5$ to the left of $x$ .

$y = 6 x^{3} + 5 x^{2} - 12 x - \frac{5 x}{3} + 5$

Step 3

To write $- 12 x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = 6 x^{3} + 5 x^{2} - 12 x \cdot \frac{3}{3} - \frac{5 x}{3} + 5$

Step 4

Combine $- 12 x$ and $\frac{3}{3}$ .

$y = 6 x^{3} + 5 x^{2} + \frac{- 12 x \cdot 3}{3} - \frac{5 x}{3} + 5$

Step 5

Combine the numerators over the common denominator.

$y = 6 x^{3} + 5 x^{2} + \frac{- 12 x \cdot 3 - 5 x}{3} + 5$

Step 6

Simplify each term.

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Step 6.1

Simplify the numerator.

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Step 6.1.1

Factor $x$ out of $- 12 x \cdot 3 - 5 x$ .

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Step 6.1.1.1

Factor $x$ out of $- 12 x \cdot 3$ .

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

Step 6.1.1.2

Factor $x$ out of $- 5 x$ .

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

Step 6.1.1.3

Factor $x$ out of $x (- 12 \cdot 3) + x \cdot - 5$ .

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

Step 6.1.2

Multiply $- 12$ by $3$ .

$y = 6 x^{3} + 5 x^{2} + \frac{x (- 36 - 5)}{3} + 5$

Step 6.1.3

Subtract $5$ from $- 36$ .

$y = 6 x^{3} + 5 x^{2} + \frac{x \cdot - 41}{3} + 5$

Step 6.2

Move $- 41$ to the left of $x$ .

$y = 6 x^{3} + 5 x^{2} + \frac{- 41 \cdot x}{3} + 5$

Step 6.3

Move the negative in front of the fraction.

$y = 6 x^{3} + 5 x^{2} - \frac{41 x}{3} + 5$

Step 7

The given equation $y = 6 x^{3} + 5 x^{2} - \frac{41 x}{3} + 5$ can not be written as $y = k x^{2}$ , so $y$ doesn't vary directly with $x^{2}$ .

$y$ doesn't vary directly with $x$