Algebra Examples

$5 \pm 3 i$

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 $x = 5 \pm 3 i$ was found by solving for $x$ when $x - (5 \pm 3 i) = y$ and $y = 0$ .

The factor is $x - (5 \pm 3 i)$

Step 3

The root at $x = - (5 \pm 3 i)$ was found by solving for $x$ when $x - (- (5 \pm 3 i)) = y$ and $y = 0$ .

The factor is $x + 5 \pm 3 i$

Step 4

Combine all the factors into a single equation.

$y = (x - (5 \pm 3 i)) (x + 5 \pm 3 i)$

Step 5

Apply the distributive property.

$y = x (x + 5 \pm 3 i) - (5 \pm 3 i) (x + 5 \pm 3 i)$

Step 6