Degree of a Polynomial

Test Preparation
1

<p>If a function below is a polynomial state its degree, and if it is not a polynomial explain why:</p>

<p>A) g(t)= t + 3t^2 - 5t^4 + 7</p>

<p>ANSWER: 4</p>

<p>B) q(x)= 5x^3 + 2x - 5 sqrt(x)</p>

<p>ANSWER: UNSURE</p>

<p>C) f(x)= 5</p>

<p>ANSWER: 0</p>

<p>D) v(y)= e^(3y) + 6y^5</p>

<p>ANSWER: UNSURE</p>

<p>I am unsure about B and D. Can someone please help me?</p>

2

<p>I don't think either of them are polynomials.</p>

<p>For B, sqrt(x) is the same as x^(1/2), and in polynomials the exponent must be an integer, right? Same with D, you've got a constant to the power of a variable, it needs to be an integer.</p>

<p>I believe neither is a polynomial.</p>

3

<p>Can someone verify that a polynomial function must contain ONLY integral powers?</p>

4

<p>B and D are functions as they pass the verticle line test.</p>

5

<p>
[quote]
B and D are functions as they pass the verticle line test.

[/quote]

Yes, we know this, but are these "polynomial" functions and to what degree? Also, can someone verify that a polynomial function must conatain ONLY integral powers as post #2 has said?</p>

6

<p>C is not a polynomial, it is a monomial. Polynomial generally refers to having more terms that 2 or 3 (because after that the names get confusing lol), although technically binomials and above are polynomials. But yes the exponents do need to be integers.</p>

<p>monomial, binomial, trinomial, polynomial</p>

<p>Any number alone (like 5) is a monomial.</p>

7

<p>


</p>

<p>hahhahahahahahahahha. Wrong. Monomials are polynomials.</p>

<p>
[quote]

pol·y·no·mi·al
Mathematics.</p>

<ol>
<li>An algebraic expression consisting of one or more summed terms, each term consisting of a constant multiplier and one or more variables raised to integral powers. For example, x^2 − 5x + 6 and 2p^3q + y are polynomials. Also called multinomial.

[/quote]
</li>
</ol>

8

<p>Yeah, anonymous is right, a polynomial can be single-termed.</p>

<p>And his definition pretty clearly states that the powers must be integral, so square roots and 6y are both out.</p>

9

<p>why is 6y out? please explain</p>

10

<p>
[quote]
why is 6y out? please explain

[/quote]

I think he means 3y from the constant e.</p>

11

<p>B) not a Polynomial..because x is raised to a non-whole number ( 5 Sqrt (x) is the same as 5x^(1/2) ) </p>

<p>D)not a polynomial because e is raised to a varible not a constant ( i am 90% sure about this .....need to check) </p>

<p>
[quote]
Can someone verify that a polynomial function must contain ONLY integral powers?

[/quote]
</p>

<p>there you go (From Wikipedia)</p>

<p>
[quote]
In mathematics, a polynomial is an expression in which a finite number of constants and variables are combined using only addition, subtraction, multiplication, and positive whole number exponents (raising to a power).

[/quote]
</p>

12

<p>Woops, yeah, I meant the 3y</p>

13

<p>Just so you don't get confused easily, always keep in mind that polynomials must have the following form:</p>

<p>f(x) = a(sub n) x(sub n) + a(sub n-1) x(sub n-1) + ... + a(sub 1) x + a(sub 0)</p>

<p>where n must be a non-negative integer (i.e., a whole number or zero). The coefficients a(sub n), a(sub n-1), ..., a(sub 1), a(sub 0) must be real numbers.</p>

<p>The degree of the polynomial function is the highest value of n where a(sub n) is not zero.</p>

<p>Using the above as a guideline, we can quickly tell that:</p>

<p>A is a polynomial with a degree of 4.</p>

<p>B is not a polynomial since - 5 sqrt(x) equals to -5 x^(1/2), and (1/2) is not an integer.</p>

<p>C is technically a polynomial with a degree of 0.</p>

<p>D is not a polynomial since its form does not follow the general form given above.</p>

14

<p>The above form should be:</p>

<p>f(x) = a(sub n) x^n + a(sub n-1) x^(n-1) + ... + a(sub 1) x + a(sub 0)</p>