I'm helping a high school student prepare for an exam, and I'm unsure how to answer this...

Why is $x^3+2x^2$ not quadratic? I thought anything that had a power of 2 was quadratic.

  • 2
    $\begingroup$ It's not quadratic becouse it have power that is higher then $2$. Form is quadratic, when the highest power is $2$. $\endgroup$ Jun 11, 2013 at 20:16
  • 2
    $\begingroup$ The power $2$ must occur in the polynomial, and it must be the highest power of the variable in the expression. $\endgroup$ Jun 11, 2013 at 20:16

2 Answers 2


A quadratic must be a polynomial and it must be of degree $2$.

The degree of a polynomial in $x$ is the highest power of $x$ appearing in the function.

So we have that your function is a degree $3$ polynomial, also known as a cubic.

  • $\begingroup$ Links and all! :-) +1 $\endgroup$
    – Amzoti
    Jun 12, 2013 at 0:27
  • $\begingroup$ You're so sweet, @Babak. Yes, I am winding down, preparing for bed. You go get 'em! Kill those questions! $\endgroup$
    – amWhy
    Jun 13, 2013 at 4:57

It only depends on the highest order term. In your case, it is a third order polynomial. If it were just $ax^2+bx+c$ it would be quadratic

  • 1
    $\begingroup$ Your first sentence is correct, if it is a polynomial. $\endgroup$
    – vadim123
    Jun 11, 2013 at 20:20

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.