Algebra Examples

$x^{2} + p x + q = (x - 13) (x + 1)$

Step 1

Simplify $(x - 13) (x + 1)$ .

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Step 1.1

Rewrite.

$x^{2} + p x + q = 0 + 0 + (x - 13) (x + 1)$

Step 1.2

Simplify by adding zeros.

$x^{2} + p x + q = (x - 13) (x + 1)$

Step 1.3

Expand $(x - 13) (x + 1)$ using the FOIL Method.

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Step 1.3.1

Apply the distributive property.

$x^{2} + p x + q = x (x + 1) - 13 (x + 1)$

Step 1.3.2

Apply the distributive property.

$x^{2} + p x + q = x \cdot x + x \cdot 1 - 13 (x + 1)$

Step 1.3.3

Apply the distributive property.

$x^{2} + p x + q = x \cdot x + x \cdot 1 - 13 x - 13 \cdot 1$

Step 1.4

Simplify and combine like terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

Multiply $x$ by $x$ .

$x^{2} + p x + q = x^{2} + x \cdot 1 - 13 x - 13 \cdot 1$

Step 1.4.1.2

Multiply $x$ by $1$ .

$x^{2} + p x + q = x^{2} + x - 13 x - 13 \cdot 1$

Step 1.4.1.3

Multiply $- 13$ by $1$ .

$x^{2} + p x + q = x^{2} + x - 13 x - 13$

Step 1.4.2

Subtract $13 x$ from $x$ .

$x^{2} + p x + q = x^{2} - 12 x - 13$

Step 2

Move all terms not containing $p$ to the right side of the equation.

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Step 2.1

Subtract $x^{2}$ from both sides of the equation.

$p x + q = x^{2} - 12 x - 13 - x^{2}$

Step 2.2

Subtract $q$ from both sides of the equation.

$p x = x^{2} - 12 x - 13 - x^{2} - q$

Step 2.3

Combine the opposite terms in $x^{2} - 12 x - 13 - x^{2} - q$ .

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Step 2.3.1

Subtract $x^{2}$ from $x^{2}$ .

$p x = - 12 x - 13 + 0 - q$

Step 2.3.2

Add $- 12 x - 13$ and $0$ .

$p x = - 12 x - 13 - q$

Step 3

Divide each term in $p x = - 12 x - 13 - q$ by $x$ and simplify.

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Step 3.1

Divide each term in $p x = - 12 x - 13 - q$ by $x$ .

$\frac{p x}{x} = \frac{- 12 x}{x} + \frac{- 13}{x} + \frac{- q}{x}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $x$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{p x}{x} = \frac{- 12 x}{x} + \frac{- 13}{x} + \frac{- q}{x}$

Step 3.2.1.2

Divide $p$ by $1$ .

$p = \frac{- 12 x}{x} + \frac{- 13}{x} + \frac{- q}{x}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Cancel the common factor of $x$ .

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Step 3.3.1.1.1

Cancel the common factor.

$p = \frac{- 12 x}{x} + \frac{- 13}{x} + \frac{- q}{x}$

Step 3.3.1.1.2

Divide $- 12$ by $1$ .

$p = - 12 + \frac{- 13}{x} + \frac{- q}{x}$

Step 3.3.1.2

Move the negative in front of the fraction.

$p = - 12 - \frac{13}{x} + \frac{- q}{x}$

Step 3.3.1.3

Move the negative in front of the fraction.

$p = - 12 - \frac{13}{x} - \frac{q}{x}$