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A polynomial function of degree and leading coefficient $ a_n $ is a function of the form $ f(x) = a_n x^n + a_{n-1} x^{n-1} + \cdots + a_1 x + a_0 (a_n \neq 0) $ where $ n $ is a ________ _________ and $ a_n, a_{n-1}, \cdots , a_1, a_0 $ are ________ numbers.

Nonnegative integer, real

Algebra

Chapter 2

Polynomial and Rational Functions

Section 1

Quadratic Functions and Models

Quadratic Functions

Complex Numbers

Polynomials

Rational Functions

Missouri State University

Campbell University

Lectures

01:32

In mathematics, the absolu…

01:11

00:42

A polynomial function with…

00:29

00:44

Fill in the blank.Func…

01:01

Fill in the blank.A fu…

00:24

Fill in the blank.The …

00:51

The general polynomial of …

01:30

01:13

Find a polynomial $f(x)$ w…

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01:20

00:14

Fill in the blanks.A p…

00:52

01:07

02:26

00:28

00:37

02:55

Express the polynomial $f(…

00:43

Fill in the blanks.A _…

00:17

Fill in the blank:If $…

00:13

Use the Laws of Logarithms…

in this problem, they give us the formula for a general polynomial. So this is a degree and polynomial So they're telling us that here. So if you want to call this a degree and polynomial, then we need the leading coefficient to be non zero. So this is what we would call the leading coefficient. Even though they're not asking for that, I just want to point that out. So we want to know what kind of number and has to be. So it's the smallest and could be well, you can look at a polynomial of this form if we just take the constant term. So you don't see an ex here or if you really want you could think of this is being X to the zero hour, as you could see in each case, the sub script on the A's matches with the power of the ex, so here to subscript zero. So that's the same power of X. And so the smallest it could be a zero. Otherwise we could take one to all the way up to any number. And so in this case, it has to be a whole number. So I'll remind you What? Those are thes air. The numbers of the form zero one, two, three and so on. And how about the coefficients over here? These are the coefficients of our polynomial. What type of numbers or these were just needs to be real numbers. And there's our final answer.

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