Algebra Examples

$- 4 x^{3} + x^{2} - 6 x + 8$

Step 1

Regroup terms.

$- 4 x^{3} + x^{2} - 6 x + 8$

Step 2

Factor $x^{2} - 6 x + 8$ using the AC method.

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Step 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 $8$ and whose sum is $- 6$ .

$- 4, - 2$

Step 2.2

Write the factored form using these integers.

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

Step 3

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

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Step 3.1

Factor $- 1$ out of $- 4 x^{3}$ .

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

Step 3.2

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

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

Step 3.3

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

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

Step 4

Expand $(- x + 4) (x - 2)$ using the FOIL Method.

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Step 4.1

Apply the distributive property.

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

Step 4.2

Apply the distributive property.

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

Step 4.3

Apply the distributive property.

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

Step 5

Simplify and combine like terms.

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Step 5.1

Simplify each term.

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Step 5.1.1

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

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Step 5.1.1.1

Move $x$ .

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

Step 5.1.1.2

Multiply $x$ by $x$ .

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

Step 5.1.2

Multiply $- 2$ by $- 1$ .

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

Step 5.1.3

Multiply $4$ by $- 2$ .

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

Step 5.2

Add $2 x$ and $4 x$ .

$- (4 x^{3} - x^{2} + 6 x - 8)$