Precalculus 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

\frac{f (x)}{g (x)}

$\frac{f (x)}{g (x)}$ .

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

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

Step 2

Factor

2

$2$ out of

2 x - 2

$2 x - 2$ .

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Step 2.1

Factor

2

$2$ out of

2 x

$2 x$ .

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

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

Step 2.2

Factor

2

$2$ out of

- 2

$- 2$ .

\frac{x^{4} + x^{3} - 11 x^{2} - 5 x + 30}{2 (x) + 2 (- 1)}

$\frac{x^{4} + x^{3} - 11 x^{2} - 5 x + 30}{2 (x) + 2 (- 1)}$

Step 2.3

Factor

2

$2$ out of

2 (x) + 2 (- 1)

$2 (x) + 2 (- 1)$ .

\frac{x^{4} + x^{3} - 11 x^{2} - 5 x + 30}{2 (x - 1)}

$\frac{x^{4} + x^{3} - 11 x^{2} - 5 x + 30}{2 (x - 1)}$

\frac{x^{4} + x^{3} - 11 x^{2} - 5 x + 30}{2 (x - 1)}

$\frac{x^{4} + x^{3} - 11 x^{2} - 5 x + 30}{2 (x - 1)}$

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