Algebra Examples

$\frac{4 x^{3} - 12 x^{2} + 8 x}{- 4 x}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $4 x$ out of $4 x^{3} - 12 x^{2} + 8 x$ .

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Step 1.1.1

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

$\frac{4 x (x^{2}) - 12 x^{2} + 8 x}{- 4 x}$

Step 1.1.2

Factor $4 x$ out of $- 12 x^{2}$ .

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

Step 1.1.3

Factor $4 x$ out of $8 x$ .

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

Step 1.1.4

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

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

Step 1.1.5

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

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

Step 1.2

Factor $x^{2} - 3 x + 2$ using the AC method.

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Step 1.2.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $2$ and whose sum is $- 3$ .

$- 2, - 1$

Step 1.2.2

Write the factored form using these integers.

$\frac{4 x ((x - 2) (x - 1))}{- 4 x}$

$\frac{4 x (x - 2) (x - 1)}{- 4 x}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

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

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Step 2.1.1

Factor $4$ out of $4 x (x - 2) (x - 1)$ .

$\frac{4 ((x (x - 2)) (x - 1))}{- 4 x}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $4$ out of $- 4 x$ .

$\frac{4 ((x (x - 2)) (x - 1))}{4 (- x)}$

Step 2.1.2.2

Cancel the common factor.

$\frac{4 ((x (x - 2)) (x - 1))}{4 (- x)}$

Step 2.1.2.3

Rewrite the expression.

$\frac{(x (x - 2)) (x - 1)}{- x}$

Step 2.2

Cancel the common factor of $x$ .

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Step 2.2.1

Cancel the common factor.

$\frac{x (x - 2) (x - 1)}{- x}$

Step 2.2.2

Rewrite the expression.

$\frac{(x - 2) (x - 1)}{- 1}$

Step 2.2.3

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

$- 1 \cdot ((x - 2) (x - 1))$

Step 2.3

Rewrite $- 1 \cdot ((x - 2) (x - 1))$ as $- ((x - 2) (x - 1))$ .

$- ((x - 2) (x - 1))$

Step 3

Expand $(x - 2) (x - 1)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

$- (x (x - 1) - 2 (x - 1))$

Step 3.2

Apply the distributive property.

$- (x \cdot x + x \cdot - 1 - 2 (x - 1))$

Step 3.3

Apply the distributive property.

$- (x \cdot x + x \cdot - 1 - 2 x - 2 \cdot - 1)$

Step 4

Simplify and combine like terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $x$ by $x$ .

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

Step 4.1.2

Move $- 1$ to the left of $x$ .

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

Step 4.1.3

Rewrite $- 1 x$ as $- x$ .

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

Step 4.1.4

Multiply $- 2$ by $- 1$ .

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

Step 4.2

Subtract $2 x$ from $- x$ .

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

Step 5

Apply the distributive property.

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

Step 6

Simplify.

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Step 6.1

Multiply $- 3$ by $- 1$ .

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

Step 6.2

Multiply $- 1$ by $2$ .

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