Question

Is y=x^4+3x^2 even, odd, or neither?

Answer 1

EVEN

Explanation:

the product of odd numbers is always odd

the product of even numbers is always even

the product of odd number and even one is always even

the sum of two odd numbers is always even

and the sum of two even numbers is always even

so if x is even number we have:

x²=x•x - even number

x⁴=x²•x² - even number

3x²=3•x² - even number

y = x⁴+3x² - even number

and if x is odd number we have:

x²=x•x - odd number

x⁴=x²•x² - odd number

3x²=3•x² - odd number

y = x⁴+3x² - even number