How Do You Differentiate Between Polynomial and Rational Algebraic Functions?

[JasonRox]

How can you tell the two apart?

Here are some examples in the book:

1. 3x^3 + 2x + 1

2. 3x^2 + (x + 1)^1/2

3. \frac{2x + 3}{x^2 + 1}

4. (\frac{x}{x + 1})^X

 

[JonF]

You just need to distribute.

#2 distributed is:
3x^2 + 1/2x + 1/2

and #4 distributed is:
\frac{x^2}{x+1}

After distributing all four are very obviously different

 

[JonF]

After relooking at your post I realized that you may not be comparing equations but instead classifying them.

A polynomial can be express as ax^n + bx^(n-1) + cx^(n-2) + dx^(n-3) … +c

I’d have to look up the definition for a “rational algebraic expression” but going from memory it is any expression that has only algebraic terms?

 

[expscv]

the polynomial 's power must be postive interger . that's the difference

 

[uart]

A Polynomial (in x) is a linear combination of non-negative powers of x.

A rational algebraic function is just a fraction N(x)/D(x) where N and D are both polynomials.

In your examples 1. and 2. are polynomials while 3. and 4. are rational algebraic functions.

 

[expscv]

A Polynomial (in x) is a linear combination of non-negative powers of x.

A rational algebraic function is just a fraction N(x)/D(x) where N and D are both polynomials.

In your examples 1. and 2. are polynomials while 3. and 4. are rational algebraic functions.

oh? i though the power of polynomial must be interger, i go check

 

[uart]

oh? i though the power of polynomial must be interger, i go check

No need to check you're correct. It was just a slip, I meant to say non-negative integer but only type non-negative.

 

[JasonRox]

Thanks, guys.

 

[krab]

A polynomial can be express as ax^n + bx^(n-1) + cx^(n-2) + dx^(n-3) ? +c

JonF: use curly brackets to apply something (in this case ^) to an expression.
ax^n + bx^{n-1} + cx^{n-2} + dx^{n-3}...+c

 

[Muzza]

Why would the constant term be equal to the coefficient in front of x^(n - 2)? ;)

 

[JonF]

argh, thank you