Algebra Examples

10

$10$ ,

1

$1$

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 = 10

$x = 10$ was found by solving for

x

$x$ when

x - (10) = y

$x - (10) = y$ and

y = 0

$y = 0$ .

The factor is

x - 10

$x - 10$

Step 3

The root at

x = 1

$x = 1$ was found by solving for

x

$x$ when

x - (1) = y

$x - (1) = y$ and

y = 0

$y = 0$ .

The factor is

x - 1

$x - 1$

Step 4

Combine all the factors into a single equation.

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

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

Step 5

Multiply all the factors to simplify the equation

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

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

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Step 5.1

Expand

(x - 10) (x - 1)

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

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Step 5.1.1

Apply the distributive property.

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

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

Step 5.1.2

Apply the distributive property.

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

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

Step 5.1.3

Apply the distributive property.

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

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

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

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

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

$x$ by

x

$x$ .

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

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

Step 5.2.1.2

Move

- 1

$- 1$ to the left of

x

$x$ .

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

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

Step 5.2.1.3

Rewrite

- 1 x

$- 1 x$ as

- x

$- x$ .

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

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

Step 5.2.1.4

Multiply

- 10

$- 10$ by

- 1

$- 1$ .

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

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

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

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

Step 5.2.2

Subtract

10 x

$10 x$ from

- x

$- x$ .

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

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

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

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

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

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

Step 6

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