Examples

x = 2

$x = 2$ ,

x = - 2

$x = - 2$ ,

x = 1

$x = 1$

Step 1

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

0

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

0

$0$ .

(x - 2) (x - (- 2)) (x - 1) = 0

$(x - 2) (x - (- 2)) (x - 1) = 0$

Step 2

Simplify.

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Step 2.1

Expand

(x - 2) (x + 2)

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

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Step 2.1.1

Apply the distributive property.

(x (x + 2) - 2 (x + 2)) (x - 1) = 0

$(x (x + 2) - 2 (x + 2)) (x - 1) = 0$

Step 2.1.2

Apply the distributive property.

(x \cdot x + x \cdot 2 - 2 (x + 2)) (x - 1) = 0

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

Step 2.1.3

Apply the distributive property.

(x \cdot x + x \cdot 2 - 2 x - 2 \cdot 2) (x - 1) = 0

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

(x \cdot x + x \cdot 2 - 2 x - 2 \cdot 2) (x - 1) = 0

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

Step 2.2

Simplify terms.

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Step 2.2.1

Combine the opposite terms in

x \cdot x + x \cdot 2 - 2 x - 2 \cdot 2

$x \cdot x + x \cdot 2 - 2 x - 2 \cdot 2$ .

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Step 2.2.1.1

Reorder the factors in the terms

x \cdot 2

$x \cdot 2$ and

- 2 x

$- 2 x$ .

(x \cdot x + 2 x - 2 x - 2 \cdot 2) (x - 1) = 0

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

Step 2.2.1.2

Subtract

2 x

$2 x$ from

2 x

$2 x$ .

(x \cdot x + 0 - 2 \cdot 2) (x - 1) = 0

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

Step 2.2.1.3

Add

x \cdot x

$x \cdot x$ and

0

$0$ .

(x \cdot x - 2 \cdot 2) (x - 1) = 0

$(x \cdot x - 2 \cdot 2) (x - 1) = 0$

(x \cdot x - 2 \cdot 2) (x - 1) = 0

$(x \cdot x - 2 \cdot 2) (x - 1) = 0$

Step 2.2.2

Simplify each term.

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Step 2.2.2.1

Multiply

x

$x$ by

x

$x$ .

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

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

Step 2.2.2.2

Multiply

- 2

$- 2$ by

2

$2$ .

(x^{2} - 4) (x - 1) = 0

$(x^{2} - 4) (x - 1) = 0$

(x^{2} - 4) (x - 1) = 0

$(x^{2} - 4) (x - 1) = 0$

(x^{2} - 4) (x - 1) = 0

$(x^{2} - 4) (x - 1) = 0$

Step 2.3

Expand

(x^{2} - 4) (x - 1)

$(x^{2} - 4) (x - 1)$ using the FOIL Method.

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Step 2.3.1

Apply the distributive property.

x^{2} (x - 1) - 4 (x - 1) = 0

$x^{2} (x - 1) - 4 (x - 1) = 0$

Step 2.3.2

Apply the distributive property.

x^{2} x + x^{2} \cdot - 1 - 4 (x - 1) = 0

$x^{2} x + x^{2} \cdot - 1 - 4 (x - 1) = 0$

Step 2.3.3

Apply the distributive property.

x^{2} x + x^{2} \cdot - 1 - 4 x - 4 \cdot - 1 = 0

$x^{2} x + x^{2} \cdot - 1 - 4 x - 4 \cdot - 1 = 0$

x^{2} x + x^{2} \cdot - 1 - 4 x - 4 \cdot - 1 = 0

$x^{2} x + x^{2} \cdot - 1 - 4 x - 4 \cdot - 1 = 0$

Step 2.4

Simplify each term.

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Step 2.4.1

Multiply

x^{2}

$x^{2}$ by

x

$x$ by adding the exponents.

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Step 2.4.1.1

Multiply

x^{2}

$x^{2}$ by

x

$x$ .

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Step 2.4.1.1.1

Raise

x

$x$ to the power of

1

$1$ .

x^{2} x + x^{2} \cdot - 1 - 4 x - 4 \cdot - 1 = 0

$x^{2} x + x^{2} \cdot - 1 - 4 x - 4 \cdot - 1 = 0$

Step 2.4.1.1.2

Use the power rule

a^{m} a^{n} = a^{m + n}

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

x^{2 + 1} + x^{2} \cdot - 1 - 4 x - 4 \cdot - 1 = 0

$x^{2 + 1} + x^{2} \cdot - 1 - 4 x - 4 \cdot - 1 = 0$

x^{2 + 1} + x^{2} \cdot - 1 - 4 x - 4 \cdot - 1 = 0

$x^{2 + 1} + x^{2} \cdot - 1 - 4 x - 4 \cdot - 1 = 0$

Step 2.4.1.2

Add

2

$2$ and

1

$1$ .

x^{3} + x^{2} \cdot - 1 - 4 x - 4 \cdot - 1 = 0

$x^{3} + x^{2} \cdot - 1 - 4 x - 4 \cdot - 1 = 0$

x^{3} + x^{2} \cdot - 1 - 4 x - 4 \cdot - 1 = 0

$x^{3} + x^{2} \cdot - 1 - 4 x - 4 \cdot - 1 = 0$

Step 2.4.2

Move

- 1

$- 1$ to the left of

x^{2}

$x^{2}$ .

x^{3} - 1 \cdot x^{2} - 4 x - 4 \cdot - 1 = 0

$x^{3} - 1 \cdot x^{2} - 4 x - 4 \cdot - 1 = 0$

Step 2.4.3

Rewrite

- 1 x^{2}

$- 1 x^{2}$ as

- x^{2}

$- x^{2}$ .

x^{3} - x^{2} - 4 x - 4 \cdot - 1 = 0

$x^{3} - x^{2} - 4 x - 4 \cdot - 1 = 0$

Step 2.4.4

Multiply

- 4

$- 4$ by

- 1

$- 1$ .

x^{3} - x^{2} - 4 x + 4 = 0

$x^{3} - x^{2} - 4 x + 4 = 0$

x^{3} - x^{2} - 4 x + 4 = 0

$x^{3} - x^{2} - 4 x + 4 = 0$

x^{3} - x^{2} - 4 x + 4 = 0

$x^{3} - x^{2} - 4 x + 4 = 0$

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