Finite Math Examples

x^{2} - 3 x - 4 = (x - a) (x - b)

$x^{2} - 3 x - 4 = (x - a) (x - b)$

Step 1

Subtract

(x - a) (x - b)

$(x - a) (x - b)$ from both sides of the equation.

x^{2} - 3 x - 4 - (x - a) (x - b) = 0

$x^{2} - 3 x - 4 - (x - a) (x - b) = 0$

Step 2

Simplify

x^{2} - 3 x - 4 - (x - a) (x - b)

$x^{2} - 3 x - 4 - (x - a) (x - b)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

x^{2} - 3 x - 4 + (- x - - a) (x - b) = 0

$x^{2} - 3 x - 4 + (- x - - a) (x - b) = 0$

Step 2.1.2

Multiply

- - a

$- - a$ .

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Step 2.1.2.1

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

x^{2} - 3 x - 4 + (- x + 1 a) (x - b) = 0

$x^{2} - 3 x - 4 + (- x + 1 a) (x - b) = 0$

Step 2.1.2.2

Multiply

a

$a$ by

1

$1$ .

x^{2} - 3 x - 4 + (- x + a) (x - b) = 0

$x^{2} - 3 x - 4 + (- x + a) (x - b) = 0$

x^{2} - 3 x - 4 + (- x + a) (x - b) = 0

$x^{2} - 3 x - 4 + (- x + a) (x - b) = 0$

Step 2.1.3

Expand

(- x + a) (x - b)

$(- x + a) (x - b)$ using the FOIL Method.

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Step 2.1.3.1

Apply the distributive property.

x^{2} - 3 x - 4 - x (x - b) + a (x - b) = 0

$x^{2} - 3 x - 4 - x (x - b) + a (x - b) = 0$

Step 2.1.3.2

Apply the distributive property.

x^{2} - 3 x - 4 - x \cdot x - x (- b) + a (x - b) = 0

$x^{2} - 3 x - 4 - x \cdot x - x (- b) + a (x - b) = 0$

Step 2.1.3.3

Apply the distributive property.

x^{2} - 3 x - 4 - x \cdot x - x (- b) + a x + a (- b) = 0

$x^{2} - 3 x - 4 - x \cdot x - x (- b) + a x + a (- b) = 0$

x^{2} - 3 x - 4 - x \cdot x - x (- b) + a x + a (- b) = 0

$x^{2} - 3 x - 4 - x \cdot x - x (- b) + a x + a (- b) = 0$

Step 2.1.4

Simplify each term.

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Step 2.1.4.1

Multiply

x

$x$ by

x

$x$ by adding the exponents.

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Step 2.1.4.1.1

Move

x

$x$ .

x^{2} - 3 x - 4 - (x \cdot x) - x (- b) + a x + a (- b) = 0

$x^{2} - 3 x - 4 - (x \cdot x) - x (- b) + a x + a (- b) = 0$

Step 2.1.4.1.2

Multiply

x

$x$ by

x

$x$ .

x^{2} - 3 x - 4 - x^{2} - x (- b) + a x + a (- b) = 0

$x^{2} - 3 x - 4 - x^{2} - x (- b) + a x + a (- b) = 0$

x^{2} - 3 x - 4 - x^{2} - x (- b) + a x + a (- b) = 0

$x^{2} - 3 x - 4 - x^{2} - x (- b) + a x + a (- b) = 0$

Step 2.1.4.2

Rewrite using the commutative property of multiplication.

x^{2} - 3 x - 4 - x^{2} - 1 \cdot - 1 x b + a x + a (- b) = 0

$x^{2} - 3 x - 4 - x^{2} - 1 \cdot - 1 x b + a x + a (- b) = 0$

Step 2.1.4.3

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

x^{2} - 3 x - 4 - x^{2} + 1 x b + a x + a (- b) = 0

$x^{2} - 3 x - 4 - x^{2} + 1 x b + a x + a (- b) = 0$

Step 2.1.4.4

Multiply

x

$x$ by

1

$1$ .

x^{2} - 3 x - 4 - x^{2} + x b + a x + a (- b) = 0

$x^{2} - 3 x - 4 - x^{2} + x b + a x + a (- b) = 0$

Step 2.1.4.5

Rewrite using the commutative property of multiplication.

x^{2} - 3 x - 4 - x^{2} + x b + a x - a b = 0

$x^{2} - 3 x - 4 - x^{2} + x b + a x - a b = 0$

x^{2} - 3 x - 4 - x^{2} + x b + a x - a b = 0

$x^{2} - 3 x - 4 - x^{2} + x b + a x - a b = 0$

x^{2} - 3 x - 4 - x^{2} + x b + a x - a b = 0

$x^{2} - 3 x - 4 - x^{2} + x b + a x - a b = 0$

Step 2.2

Combine the opposite terms in

x^{2} - 3 x - 4 - x^{2} + x b + a x - a b

$x^{2} - 3 x - 4 - x^{2} + x b + a x - a b$ .

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Step 2.2.1

Subtract

x^{2}

$x^{2}$ from

x^{2}

$x^{2}$ .

- 3 x - 4 + 0 + x b + a x - a b = 0

$- 3 x - 4 + 0 + x b + a x - a b = 0$

Step 2.2.2

Add

- 3 x - 4

$- 3 x - 4$ and

0

$0$ .

- 3 x - 4 + x b + a x - a b = 0

$- 3 x - 4 + x b + a x - a b = 0$

- 3 x - 4 + x b + a x - a b = 0

$- 3 x - 4 + x b + a x - a b = 0$

- 3 x - 4 + x b + a x - a b = 0

$- 3 x - 4 + x b + a x - a b = 0$

Step 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.