How this calculation works
Classify a real cubic-or-lower polynomial by its nonzero coefficient powers.
THE FORMULA
Even powers are unchanged by x→−x. Odd powers change sign.A worked example
3x²−2 has only even powers, so f(−x)=f(x).
Good to know
The zero polynomial is both even and odd.
Reference: OpenStax Algebra and Trigonometry (opens in a new tab) ↗
Read the result
Classify a real cubic-or-lower polynomial by its nonzero coefficient powers.
The primary result is labeled “Symmetry”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The zero polynomial is both even and odd.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
3x²−2 has only even powers, so f(−x)=f(x).
Which rule does this calculator apply?
Even powers are unchanged by x→−x. Odd powers change sign.