Determine if Odd, Even, or Neither 5x^4+3x^2+2

$5 x^{4} + 3 x^{2} + 2$

Step 1

Write $5 x^{4} + 3 x^{2} + 2$ as a function.

$f (x) = 5 x^{4} + 3 x^{2} + 2$

Step 2

Find $f (- x)$ .

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

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

Simplify each term.

Apply the product rule to $- x$ .

$f (- x) = 5 ({(- 1)}^{4} x^{4}) + 3 {(- x)}^{2} + 2$

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

$f (- x) = 5 (1 x^{4}) + 3 {(- x)}^{2} + 2$

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

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

Apply the product rule to $- x$ .

$f (- x) = 5 x^{4} + 3 ({(- 1)}^{2} x^{2}) + 2$

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

$f (- x) = 5 x^{4} + 3 (1 x^{2}) + 2$

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

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

Step 3

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

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

Since $5 x^{4} + 3 x^{2} + 2 = 5 x^{4} + 3 x^{2} + 2$ , the function is even.

The function is even

Step 4