A polynomial is an expression p(x) of the form : p(x) = a0xn+ a1xn-1 + a2xn-2 +....+an
a1,a2......are real numbers
andn is whole no.
Q1. Why did we use ....n... as a subscript for .....a.... at the last?
Notice that this is a nth degree polynomial. Hence there are n number of terms. The coefficients corresponding to are,
Notice that the subtrahend of the power of becomes the subscript of . For the last term the subtrahend is (Since the variable in the last term is, ). Therefore the corresponding coefficient should be,
I hope that I am understanding your question correctly.
p(x) = a0xn+ a1xn-1 + a2xn-2 +....+an
This is a polynomial function.
Notice that the expression looks similar to the right side of the equation you posted. It is a polynomial already, but it is not a polynomial function. If you wanted to express it as a function, you could write something like:
one small correction: a n-th degree polynomial contains n+1 terms, n terms for each power of x, and the constant term.
the degree of a polynomial p(x) is the "exponent number" of the highest power of x that occurs in it. for example, in , the highest power of x that occurs is 2 (in x squared), so this polynomial is of degree 2. so n = 2.
if we write this in the form:
we get the following values for the coefficients (this is the proper term for the "a's"):