Hello, I'm hoping someone can explain this to me:
I'm ID-ing polynomials;
-x^7-5x^4+(3/x)= not a polynomial
.25x^3+3.9x^2-(x/3)= polynomial
Why is 3/x not but x/3 is?
Thanks a bunch! :)
in polynomials, all the exponents for the variable are positive
x / 3 = 1/3 x^1
3 / x = 3 x^-1
OK, so then any unknown variable is negative, correct?
Thanks a bunch again :) I appreciate your help
Sorry, I meant to say any unknown variable in the denominator :o
Hello! I'd be happy to explain why -x^7-5x^4+(3/x) is not a polynomial, while .25x^3+3.9x^2-(x/3) is a polynomial.
A polynomial is an algebraic expression consisting of variables and coefficients, combined through addition, subtraction, and multiplication, but not division by variables. The exponents of the variables in a polynomial must be non-negative integers.
Let's break down each expression to determine if it meets the criteria for a polynomial:
1. -x^7-5x^4+(3/x):
- The expression contains addition and subtraction, which is allowed in a polynomial.
- The exponents in the variable terms (-x^7 and -5x^4) are non-negative integers, so that satisfies the requirement.
- However, the term (3/x) involves division by the variable x. Division by variables is not allowed in a polynomial, so this expression is not a polynomial.
2. .25x^3+3.9x^2-(x/3):
- The expression contains addition and subtraction, which is allowed in a polynomial.
- The coefficients (.25, 3.9, and -1/3) are numbers, so that satisfies the requirement.
- The exponents in the variable terms (x^3 and x^2) are non-negative integers.
- The term (x/3) involves division, but it is division by a constant (3), not by a variable. Division by a constant is permissible in a polynomial.
- Therefore, this expression meets all the criteria and can be classified as a polynomial.
I hope this explanation helps! Let me know if you have any further questions.