Algebra Examples

$g (x) = \frac{9 - x^{4}}{2}$

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 $9$ as $3^{2}$ .

$g (x) = \frac{3^{2} - x^{4}}{2}$

Step 2.2

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

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

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 $a = 3$ and $b = x^{2}$ .

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