Precalculus Examples

$\frac{42 x^{4} - 6 x^{3} + 36 x^{2}}{- 6 x}$

Step 1

Factor $6 x^{2}$ out of $42 x^{4} - 6 x^{3} + 36 x^{2}$ .

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Step 1.1

Factor $6 x^{2}$ out of $42 x^{4}$ .

$\frac{6 x^{2} (7 x^{2}) - 6 x^{3} + 36 x^{2}}{- 6 x}$

Step 1.2

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

$\frac{6 x^{2} (7 x^{2}) + 6 x^{2} (- x) + 36 x^{2}}{- 6 x}$

Step 1.3

Factor $6 x^{2}$ out of $36 x^{2}$ .

$\frac{6 x^{2} (7 x^{2}) + 6 x^{2} (- x) + 6 x^{2} (6)}{- 6 x}$

Step 1.4

Factor $6 x^{2}$ out of $6 x^{2} (7 x^{2}) + 6 x^{2} (- x)$ .

$\frac{6 x^{2} (7 x^{2} - x) + 6 x^{2} (6)}{- 6 x}$

Step 1.5

Factor $6 x^{2}$ out of $6 x^{2} (7 x^{2} - x) + 6 x^{2} (6)$ .

$\frac{6 x^{2} (7 x^{2} - x + 6)}{- 6 x}$

Step 2

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

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Step 2.1

Factor $6$ out of $6 x^{2} (7 x^{2} - x + 6)$ .

$\frac{6 (x^{2} (7 x^{2} - x + 6))}{- 6 x}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $6$ out of $- 6 x$ .

$\frac{6 (x^{2} (7 x^{2} - x + 6))}{6 (- x)}$

Step 2.2.2

Cancel the common factor.

$\frac{6 (x^{2} (7 x^{2} - x + 6))}{6 (- x)}$

Step 2.2.3

Rewrite the expression.

$\frac{x^{2} (7 x^{2} - x + 6)}{- x}$

Step 3

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

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Step 3.1

Factor $x$ out of $x^{2} (7 x^{2} - x + 6)$ .

$\frac{x (x (7 x^{2} - x + 6))}{- x}$

Step 3.2

Move the negative one from the denominator of $\frac{x (7 x^{2} - x + 6)}{- 1}$ .

$- 1 \cdot (x (7 x^{2} - x + 6))$

Step 4

Rewrite $- 1 \cdot (x (7 x^{2} - x + 6))$ as $- (x (7 x^{2} - x + 6))$ .

$- (x (7 x^{2} - x + 6))$

Step 5

Apply the distributive property.

$- (x (7 x^{2}) + x (- x) + x \cdot 6)$

Step 6

Simplify.

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Step 6.1

Rewrite using the commutative property of multiplication.

$- (7 x \cdot x^{2} + x (- x) + x \cdot 6)$

Step 6.2

Rewrite using the commutative property of multiplication.

$- (7 x \cdot x^{2} - x \cdot x + x \cdot 6)$

Step 6.3

Move $6$ to the left of $x$ .

$- (7 x \cdot x^{2} - x \cdot x + 6 \cdot x)$

Step 7

Simplify each term.

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Step 7.1

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

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Step 7.1.1

Move $x^{2}$ .

$- (7 (x^{2} x) - x \cdot x + 6 \cdot x)$

Step 7.1.2

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

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Step 7.1.2.1

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

$- (7 (x^{2} x^{1}) - x \cdot x + 6 \cdot x)$

Step 7.1.2.2

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

$- (7 x^{2 + 1} - x \cdot x + 6 \cdot x)$

Step 7.1.3

Add $2$ and $1$ .

$- (7 x^{3} - x \cdot x + 6 \cdot x)$

Step 7.2

Multiply $x$ by $x$ by adding the exponents.

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Step 7.2.1

Move $x$ .

$- (7 x^{3} - (x \cdot x) + 6 \cdot x)$

Step 7.2.2

Multiply $x$ by $x$ .

$- (7 x^{3} - x^{2} + 6 \cdot x)$

$- (7 x^{3} - x^{2} + 6 x)$

Step 8

Apply the distributive property.

$- (7 x^{3}) - - x^{2} - (6 x)$

Step 9

Simplify.

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Step 9.1

Multiply $7$ by $- 1$ .

$- 7 x^{3} - - x^{2} - (6 x)$

Step 9.2

Multiply $- - x^{2}$ .

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Step 9.2.1

Multiply $- 1$ by $- 1$ .

$- 7 x^{3} + 1 x^{2} - (6 x)$

Step 9.2.2

Multiply $x^{2}$ by $1$ .

$- 7 x^{3} + x^{2} - (6 x)$

Step 9.3

Multiply $6$ by $- 1$ .

$- 7 x^{3} + x^{2} - 6 x$