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What does it mean for a polynomial to be closed under addition subtraction and multiplication?
It means that you can do any of those operations, and again get a number from the set - in this case, a polynomial. Note that if you divide a polynomial by another polynomial, you will NOT always get a polynomial, so the set of polynomials is not closed under division.
What is the definition of non polynomial?
Actually, it is easier to define a polynomial as a function of a variable, x, in the form:p(x) = anxn + an-1xn-1 + ... + a2x2 + a1x + a0 where n is an integer and the ai are constants. A non-polynomial, then, is any function of x which contains one or more terms in x which are not in the form akxk.
A value of a polynomial is a value for which the polynomial is bigger or smaller than any other nearby values?
extreme
How do you find the leading term of a polynomial?
If the polynomial is in terms of the variable x, then look for the term with the biggest power (the suffix after the x) of x. That term is the leading term. So the leading term of x2 + 5 + 4x + 3x6 + 2x3 is 3x6 If you are likely to do any further work with the polynomial, it would be a good idea to arrange it in order of the descending powers of x anyway.
What is the difference between a polynomial and a quadratic equation?
Oh, dude, it's like this: all quadratic equations are polynomials, but not all polynomials are quadratic equations. A quadratic equation is a specific type of polynomial that has a degree of 2, meaning it has a highest power of x^2. So, like, all squares are rectangles, but not all rectangles are squares, you know what I mean?
