Precalculus Examples

$\frac{- 12 x^{5} + 8 x^{4} - 16 x^{3}}{- 4 x^{3}}$

Step 1

Factor $4 x^{3}$ out of $- 12 x^{5} + 8 x^{4} - 16 x^{3}$ .

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Step 1.1

Factor $4 x^{3}$ out of $- 12 x^{5}$ .

$\frac{4 x^{3} (- 3 x^{2}) + 8 x^{4} - 16 x^{3}}{- 4 x^{3}}$

Step 1.2

Factor $4 x^{3}$ out of $8 x^{4}$ .

$\frac{4 x^{3} (- 3 x^{2}) + 4 x^{3} (2 x) - 16 x^{3}}{- 4 x^{3}}$

Step 1.3

Factor $4 x^{3}$ out of $- 16 x^{3}$ .

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

Step 1.4

Factor $4 x^{3}$ out of $4 x^{3} (- 3 x^{2}) + 4 x^{3} (2 x)$ .

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

Step 1.5

Factor $4 x^{3}$ out of $4 x^{3} (- 3 x^{2} + 2 x) + 4 x^{3} (- 4)$ .

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

Step 2

Cancel the common factor of $4$ and $- 4$ .

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Step 2.1

Factor $4$ out of $4 x^{3} (- 3 x^{2} + 2 x - 4)$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

Cancel the common factor of $x^{3}$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$\frac{- 3 x^{2} + 2 x - 4}{- 1}$

Step 3.3

Move the negative one from the denominator of $\frac{- 3 x^{2} + 2 x - 4}{- 1}$ .

$- 1 \cdot (- 3 x^{2} + 2 x - 4)$

Step 4

Rewrite $- 1 \cdot (- 3 x^{2} + 2 x - 4)$ as $- (- 3 x^{2} + 2 x - 4)$ .

$- (- 3 x^{2} + 2 x - 4)$

Step 5

Apply the distributive property.

$- (- 3 x^{2}) - (2 x) - - 4$

Step 6

Simplify.

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Step 6.1

Multiply $- 3$ by $- 1$ .

$3 x^{2} - (2 x) - - 4$

Step 6.2

Multiply $2$ by $- 1$ .

$3 x^{2} - 2 x - - 4$

Step 6.3

Multiply $- 1$ by $- 4$ .

$3 x^{2} - 2 x + 4$