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 $q$ 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 $p x$ from both sides of the equation.

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

Step 2.3

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

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Step 2.3.1

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

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

Step 2.3.2

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

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