Examples

$x = 0$ ,

$x = - 1$ ,

$x = 1$

Step 1

Since the roots of an equation are the points where the solution is

$0$ , set each root as a factor of the equation that equals

$0$ .

$(x - 0) (x - (- 1)) (x - 1) = 0$

Step 2

Simplify.

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Step 2.1

Simplify by multiplying through.

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Step 2.1.1

Apply the distributive property.

$(x \cdot x + x \cdot 1) (x - 1) = 0$

Step 2.1.2

Simplify the expression.

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Step 2.1.2.1

Multiply

$x$ by

$x$ .

$(x^{2} + x \cdot 1) (x - 1) = 0$

Step 2.1.2.2

Multiply

$x$ by

$1$ .

$(x^{2} + x) (x - 1) = 0$

Step 2.2

Expand

$(x^{2} + x) (x - 1)$ using the FOIL Method.

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Step 2.2.1

Apply the distributive property.

$x^{2} (x - 1) + x (x - 1) = 0$

Step 2.2.2

Apply the distributive property.

$x^{2} x + x^{2} \cdot - 1 + x (x - 1) = 0$

Step 2.2.3

Apply the distributive property.

$x^{2} x + x^{2} \cdot - 1 + x \cdot x + x \cdot - 1 = 0$

Step 2.3

Simplify and combine like terms.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Multiply

$x^{2}$ by

$x$ by adding the exponents.

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Step 2.3.1.1.1

Multiply

$x^{2}$ by

$x$ .

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Step 2.3.1.1.1.1

Raise

$x$ to the power of

$1$ .

$x^{2} x + x^{2} \cdot - 1 + x \cdot x + x \cdot - 1 = 0$

Step 2.3.1.1.1.2

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{2 + 1} + x^{2} \cdot - 1 + x \cdot x + x \cdot - 1 = 0$

Step 2.3.1.1.2

Add

$2$ and

$1$ .

$x^{3} + x^{2} \cdot - 1 + x \cdot x + x \cdot - 1 = 0$

Step 2.3.1.2

Move

$- 1$ to the left of

$x^{2}$ .

$x^{3} - 1 \cdot x^{2} + x \cdot x + x \cdot - 1 = 0$

Step 2.3.1.3

Rewrite

$- 1 x^{2}$ as

$- x^{2}$ .

$x^{3} - x^{2} + x \cdot x + x \cdot - 1 = 0$

Step 2.3.1.4

Multiply

$x$ by

$x$ .

$x^{3} - x^{2} + x^{2} + x \cdot - 1 = 0$

Step 2.3.1.5

Move

$- 1$ to the left of

$x$ .

$x^{3} - x^{2} + x^{2} - 1 \cdot x = 0$

Step 2.3.1.6

Rewrite

$- 1 x$ as

$- x$ .

$x^{3} - x^{2} + x^{2} - x = 0$

Step 2.3.2

Add

$- x^{2}$ and

$x^{2}$ .

$x^{3} + 0 - x = 0$

Step 2.3.3

Add

$x^{3}$ and

$0$ .

$x^{3} - x = 0$

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