Thread: Definition of a polynomial

A polynomial is an expression p(x) of the form : p(x) = a₀xⁿ+ a₁x^n-1 + a₂x^n-2 +....+a_n

where

a_1,a_{2......are real numbers}

andn is whole no.

Q1. Why did we use ....n... as a subscript for .....a.... at the last?

Originally Posted by AaPa

A polynomial is an expression p(x) of the form : p(x) = a₀xⁿ+ a₁x^n-1 + a₂x^n-2 +....+a_n

where

a_1,a_{2......are real numbers}

andn is whole no.

Q1. Why did we use ....n... as a subscript for .....a.... at the last?

Hi AaPa,

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,

thanks.
please also tell me
how do we express in this form

x² + 2²

I hope that I am understanding your question correctly.

p(x) = a₀xⁿ+ a₁x^n-1 + a₂x^n-2 +....+a_n

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:

or

I want to know how to substitute the values in p(x) = a0xn+ a1xn-1 + a2xn-2 +....+an

to get

x² - 4

Originally Posted by AaPa

I want to know how to substitute the values in p(x) = a0xn+ a1xn-1 + a2xn-2 +....+an

to get

x² - 4

Compare the standard form of the nth degree polynomial, with . What are the values for the coefficients ?

That is what I am not able to tell.

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"):

.

that is:

Thank you.

1 more thing.
What do we call a polynomial that has more than 4 terms?

Originally Posted by AaPa

1 more thing.
What do we call a polynomial that has more than 4 terms?

Read this and you will find the answer: Polynomial - Wikipedia, the free encyclopedia