Examples

f (x) = x^{4} + x^{3} - 11 x^{2} - 5 x + 30

$f (x) = x^{4} + x^{3} - 11 x^{2} - 5 x + 30$ ,

g (x) = 2 x - 2

$g (x) = 2 x - 2$

Step 1

Replace the function designators with the actual functions in

f (x) - g x

$f (x) - g x$ .

x^{4} + x^{3} - 11 x^{2} - 5 x + 30 - (2 x - 2)

$x^{4} + x^{3} - 11 x^{2} - 5 x + 30 - (2 x - 2)$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

x^{4} + x^{3} - 11 x^{2} - 5 x + 30 - (2 x) - - 2

$x^{4} + x^{3} - 11 x^{2} - 5 x + 30 - (2 x) - - 2$

Step 2.2

Multiply

2

$2$ by

- 1

$- 1$ .

x^{4} + x^{3} - 11 x^{2} - 5 x + 30 - 2 x - - 2

$x^{4} + x^{3} - 11 x^{2} - 5 x + 30 - 2 x - - 2$

Step 2.3

Multiply

- 1

$- 1$ by

- 2

$- 2$ .

x^{4} + x^{3} - 11 x^{2} - 5 x + 30 - 2 x + 2

$x^{4} + x^{3} - 11 x^{2} - 5 x + 30 - 2 x + 2$

x^{4} + x^{3} - 11 x^{2} - 5 x + 30 - 2 x + 2

$x^{4} + x^{3} - 11 x^{2} - 5 x + 30 - 2 x + 2$

Step 3

Simplify by adding terms.

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Step 3.1

Subtract

2 x

$2 x$ from

- 5 x

$- 5 x$ .

x^{4} + x^{3} - 11 x^{2} - 7 x + 30 + 2

$x^{4} + x^{3} - 11 x^{2} - 7 x + 30 + 2$

Step 3.2

Add

$30$ and

$2$ .

$x^{4} + x^{3} - 11 x^{2} - 7 x + 32$

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