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Precalculus Examples

- 3

$- 3$ ,

3

$3$

Step 1

Roots are the points where the graph intercepts with the x-axis

(y = 0)

$(y = 0)$ .

y = 0

$y = 0$ at the roots

Step 2

The root at

x = - 3

$x = - 3$ was found by solving for

x

$x$ when

x - (- 3) = y

$x - (- 3) = y$ and

y = 0

$y = 0$ .

The factor is

x + 3

$x + 3$

Step 3

The root at

x = 3

$x = 3$ was found by solving for

x

$x$ when

x - (3) = y

$x - (3) = y$ and

y = 0

$y = 0$ .

The factor is

x - 3

$x - 3$

Step 4

Combine all the factors into a single equation.

y = (x + 3) (x - 3)

$y = (x + 3) (x - 3)$

Step 5

Multiply all the factors to simplify the equation

y = (x + 3) (x - 3)

$y = (x + 3) (x - 3)$ .

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Step 5.1

Expand

(x + 3) (x - 3)

$(x + 3) (x - 3)$ using the FOIL Method.

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Step 5.1.1

Apply the distributive property.

y = x (x - 3) + 3 (x - 3)

$y = x (x - 3) + 3 (x - 3)$

Step 5.1.2

Apply the distributive property.

y = x \cdot x + x \cdot - 3 + 3 (x - 3)

$y = x \cdot x + x \cdot - 3 + 3 (x - 3)$

Step 5.1.3

Apply the distributive property.

y = x \cdot x + x \cdot - 3 + 3 x + 3 \cdot - 3

$y = x \cdot x + x \cdot - 3 + 3 x + 3 \cdot - 3$

y = x \cdot x + x \cdot - 3 + 3 x + 3 \cdot - 3

$y = x \cdot x + x \cdot - 3 + 3 x + 3 \cdot - 3$

Step 5.2

Simplify terms.

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Step 5.2.1

Combine the opposite terms in

x \cdot x + x \cdot - 3 + 3 x + 3 \cdot - 3

$x \cdot x + x \cdot - 3 + 3 x + 3 \cdot - 3$ .

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Step 5.2.1.1

Reorder the factors in the terms

x \cdot - 3

$x \cdot - 3$ and

3 x

$3 x$ .

y = x \cdot x - 3 x + 3 x + 3 \cdot - 3

$y = x \cdot x - 3 x + 3 x + 3 \cdot - 3$

Step 5.2.1.2

Add

- 3 x

$- 3 x$ and

3 x

$3 x$ .

y = x \cdot x + 0 + 3 \cdot - 3

$y = x \cdot x + 0 + 3 \cdot - 3$

Step 5.2.1.3

Add

x \cdot x

$x \cdot x$ and

0

$0$ .

y = x \cdot x + 3 \cdot - 3

$y = x \cdot x + 3 \cdot - 3$

$y = x \cdot x + 3 \cdot - 3$

Step 5.2.2

Simplify each term.

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Step 5.2.2.1

Multiply

$x$ by

$x$ .

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

Step 5.2.2.2

Multiply

$3$ by

$- 3$ .

$y = x^{2} - 9$

$y = x^{2} - 9$

$y = x^{2} - 9$

$y = x^{2} - 9$

Step 6

Enter YOUR Problem

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$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$