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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.

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    $\begingroup$ 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
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    $\begingroup$ 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

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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.

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  • $\begingroup$ 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
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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

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

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