Algebra Examples

$5$ , $- 1$ , $0$

Step 1

Roots are the points where the graph intercepts with the x-axis $(y = 0)$ .

$y = 0$ at the roots

Step 2

The root at $x = 5$ was found by solving for $x$ when $x - (5) = y$ and $y = 0$ .

The factor is $x - 5$

Step 3

The root at $x = - 1$ was found by solving for $x$ when $x - (- 1) = y$ and $y = 0$ .

The factor is $x + 1$

Step 4

The root at $x = 0$ was found by solving for $x$ when $x - (0) = y$ and $y = 0$ .

The factor is $x$

Step 5

Combine all the factors into a single equation.

$y = (x - 5) (x + 1) (x)$

Step 6

Multiply all the factors to simplify the equation $y = (x - 5) (x + 1) (x)$ .

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Step 6.1

Expand $(x - 5) (x + 1)$ using the FOIL Method.

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Step 6.1.1

Apply the distributive property.

$y = (x (x + 1) - 5 (x + 1)) x$

Step 6.1.2

Apply the distributive property.

$y = (x \cdot x + x \cdot 1 - 5 (x + 1)) x$

Step 6.1.3

Apply the distributive property.

$y = (x \cdot x + x \cdot 1 - 5 x - 5 \cdot 1) x$

Step 6.2

Simplify and combine like terms.

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Step 6.2.1

Simplify each term.

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Step 6.2.1.1

Multiply $x$ by $x$ .

$y = (x^{2} + x \cdot 1 - 5 x - 5 \cdot 1) x$

Step 6.2.1.2

Multiply $x$ by $1$ .

$y = (x^{2} + x - 5 x - 5 \cdot 1) x$

Step 6.2.1.3

Multiply $- 5$ by $1$ .

$y = (x^{2} + x - 5 x - 5) x$

Step 6.2.2

Subtract $5 x$ from $x$ .

$y = (x^{2} - 4 x - 5) x$

Step 6.3

Apply the distributive property.

$y = x^{2} x - 4 x \cdot x - 5 x$

Step 6.4

Simplify.

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Step 6.4.1

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

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Step 6.4.1.1

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

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Step 6.4.1.1.1

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

$y = x^{2} x - 4 x \cdot x - 5 x$

Step 6.4.1.1.2

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

$y = x^{2 + 1} - 4 x \cdot x - 5 x$

Step 6.4.1.2

Add $2$ and $1$ .

$y = x^{3} - 4 x \cdot x - 5 x$

Step 6.4.2

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

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Step 6.4.2.1

Move $x$ .

$y = x^{3} - 4 (x \cdot x) - 5 x$

Step 6.4.2.2

Multiply $x$ by $x$ .

$y = x^{3} - 4 x^{2} - 5 x$

Step 7