Precalculus Examples

$x = 0$ , $x = - 1$ , $x = 1$

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 $0$ .

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

Simplify.

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Apply the distributive property.

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

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

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Combine $x$ and $x$

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Raise $x$ to the power of $1$ .

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

Raise $x$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $1$ .

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

Multiply $x$ by $1$ .

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

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

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Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Remove parentheses.

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

Simplify and combine like terms.

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Simplify each term.

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Multiply $x^{2}$ by $x$ by adding the exponents.

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Combine $x^{2}$ and $x$

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Raise $x$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $2$ and $1$ .

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

Move $- 1$ to the left of the expression $x^{2} \cdot - 1$ .

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

Multiply $- 1$ by $x^{2}$ .

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

Rewrite $- 1 x^{2}$ as $- x^{2}$ .

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

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

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Combine $x$ and $x$

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Raise $x$ to the power of $1$ .

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

Raise $x$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $1$ .

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

Move $- 1$ to the left of the expression $x \cdot - 1$ .

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

Multiply $- 1$ by $x$ .

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

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

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

Add $- x^{2}$ and $x^{2}$ .

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

Add $x^{3}$ and $0$ .

$x^{3} - x = 0$

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