Algebra Examples

$4$ , $- \sqrt{5}$

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 $x = 4$ was found by solving for $x$ when $x - (4) = y$ and $y = 0$ .

The factor is $x - 4$

Step 3

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

The factor is $x + \sqrt{5}$

Step 4

Combine all the factors into a single equation.

$y = (x - 4) (x + \sqrt{5})$

Step 5

Multiply all the factors to simplify the equation $y = (x - 4) (x + \sqrt{5})$ .

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Step 5.1

Expand $(x - 4) (x + \sqrt{5})$ using the FOIL Method.

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Step 5.1.1

Apply the distributive property.

$y = x (x + \sqrt{5}) - 4 (x + \sqrt{5})$

Step 5.1.2

Apply the distributive property.

$y = x \cdot x + x \sqrt{5} - 4 (x + \sqrt{5})$

Step 5.1.3

Apply the distributive property.

$y = x \cdot x + x \sqrt{5} - 4 x - 4 \sqrt{5}$

Step 5.2

Multiply $x$ by $x$ .

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

Step 6