Algebra Examples

$- 6 x^{4} + 5 x^{2}$

Step 1

Write $- 6 x^{4} + 5 x^{2}$ as a function.

$f (x) = - 6 x^{4} + 5 x^{2}$

Step 2

Find $f (- x)$ .

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Find $f (- x)$ by substituting $- x$ for all occurrence of $x$ in $f (x)$ .

$f (- x) = - 6 {(- x)}^{4} + 5 {(- x)}^{2}$

Simplify each term.

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Apply the product rule to $- x$ .

$f (- x) = - 6 ({(- 1)}^{4} x^{4}) + 5 {(- x)}^{2}$

Raise $- 1$ to the power of $4$ .

$f (- x) = - 6 (1 x^{4}) + 5 {(- x)}^{2}$

Multiply $x^{4}$ by $1$ .

$f (- x) = - 6 x^{4} + 5 {(- x)}^{2}$

Apply the product rule to $- x$ .

$f (- x) = - 6 x^{4} + 5 ({(- 1)}^{2} x^{2})$

Raise $- 1$ to the power of $2$ .

$f (- x) = - 6 x^{4} + 5 (1 x^{2})$

Multiply $x^{2}$ by $1$ .

$f (- x) = - 6 x^{4} + 5 x^{2}$

Step 3

A function is even if $f (- x) = f (x)$ .

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Check if $f (- x) = f (x)$ .

$- 6 x^{4} + 5 x^{2} = - 6 x^{4} + 5 x^{2}$

Since $- 6 x^{4} + 5 x^{2} = - 6 x^{4} + 5 x^{2}$ , the function is even.

The function is even

Step 4