Algebra Examples

$g (x) = \frac{4 - x^{6}}{3}$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$g (x) = a x^{2} + b x + c$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $4$ as $2^{2}$ .

$g (x) = \frac{2^{2} - x^{6}}{3}$

Step 2.2

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

$g (x) = \frac{2^{2} - {(x^{3})}^{2}}{3}$

Step 2.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2$ and $b = x^{3}$ .

$g (x) = \frac{(2 + x^{3}) (2 - x^{3})}{3}$