## anonymous 4 years ago Explain what are polynomials?

1. anonymous

a group of terms with a variable and a constant

2. anonymous

that's the simplest i can put it

3. anonymous

Would you like to elaborate it? @lgbasallote

4. anonymous

A polynomial is an expression that consists only of the addition, subtraction, and multiplication of non-negative integer exponents of variables and constants. They look like: x^2+2x+1, or x-50, or x^5+x^4+x^3+x^2+x+1

5. anonymous

So, you can't have 1/x as a term, for example. You can't have x^2/3 as a term either. But you can have x taken to any natural number power.

6. anonymous

can we call y=x^2 as polynomial

7. anonymous

^that's an elaboration

8. anonymous

x^2 is a polynomial. Polynomials are expressions, not equations

9. anonymous

that is a polynomial function

10. ParthKohli

Also, a negative power can't be a polynomial because then that includes division.

11. anonymous

Generally we name them after the number of terms they have, also. So if it is x+1, it's a binomial. x^2+x+1 is a trinomial. More than three terms is a polynomial.

12. anonymous

what qualifies polynomials is that the degree MUST be a non-negative integer (i.e. 1, 2, 3, 4, 5)

13. anonymous

Give me basic definations of expression ,equation and further more if you remeber? @nbouscal

14. anonymous

0 is also okay for the degree because then it's the constant term :P

15. anonymous

Expression doesn't have an =, equation does have an =

16. anonymous

so 2 is a polynomial...it has a degree of zero x is a polynomial with degree 1 x^2 is polynomial with dgree 2 and so on

17. anonymous

18. anonymous

equations contain equal signs nuff said

19. ParthKohli

2 has a degree of 1.

20. anonymous

since it has a decimal point it is not @shahzadjalbani

21. anonymous

the degree has to be INTEGERS (non-negative)...which means whole numbers

22. anonymous

the exponent has to be a natural number. A number in the set {0,1,2,...}. No fractions or decimals or negatives allowed

23. anonymous

@ParthKohli 2 has a degree of 0

24. anonymous

you look at the exponent of the variable...the exponent of the variable in 2 is 2x^0

25. ParthKohli

I see but the highest power is 1.

26. anonymous

*facepalm*

27. ParthKohli

$$\color{Black}{\Rightarrow 2^1 \times x^0 }$$

28. anonymous

Thank you all I got it .................!

29. ParthKohli

$$\color{Black}{\Rightarrow x \ne 0 \text{ btw} }$$

30. anonymous

The degree of a (nonzero) constant term is 0 source http://en.wikipedia.org/wiki/Polynomial

31. ParthKohli

Oopsie