# Can someone help me with polynomial and rational algebraic functions

1. May 2, 2004

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

2. May 3, 2004

### 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

3. May 3, 2004

### 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?

4. May 3, 2004

### expscv

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

5. May 3, 2004

### 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.

6. May 4, 2004

### expscv

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

7. May 4, 2004

### uart

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

8. May 4, 2004

### JasonRox

Thanks, guys.

9. May 4, 2004

### krab

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

10. May 4, 2004

### Muzza

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

11. May 4, 2004

### JonF

argh, thank you