Precalculus Examples

$10$ , $1$

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 $x = 10$ was found by solving for $x$ when $x - (10) = y$ and $y = 0$ .

The factor is $x - 10$

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

Combine all the factors into a single equation.

$y = (x - 10) (x - 1)$

Step 5

Multiply all the factors to simplify the equation $y = (x - 10) (x - 1)$ .

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Step 5.1

Expand $(x - 10) (x - 1)$ using the FOIL Method.

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Step 5.1.1

Apply the distributive property.

$y = x (x - 1) - 10 (x - 1)$

Step 5.1.2

Apply the distributive property.

$y = x \cdot x + x \cdot - 1 - 10 (x - 1)$

Step 5.1.3

Apply the distributive property.

$y = x \cdot x + x \cdot - 1 - 10 x - 10 \cdot - 1$

Step 5.2

Simplify and combine like terms.

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Step 5.2.1

Simplify each term.

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Step 5.2.1.1

Multiply $x$ by $x$ .

$y = x^{2} + x \cdot - 1 - 10 x - 10 \cdot - 1$

Step 5.2.1.2

Move $- 1$ to the left of $x$ .

$y = x^{2} - 1 \cdot x - 10 x - 10 \cdot - 1$

Step 5.2.1.3

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

$y = x^{2} - x - 10 x - 10 \cdot - 1$

Step 5.2.1.4

Multiply $- 10$ by $- 1$ .

$y = x^{2} - x - 10 x + 10$

Step 5.2.2

Subtract $10 x$ from $- x$ .

$y = x^{2} - 11 x + 10$

Step 6

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