Question

Can you add the exponents up and then know if its a polynomial? Im having a hard time understanding could somebody please provide me with more examples on polynomials.

Answer 1

The question is a bit vague. Do you have any specific homework problems to show?

Answer 2

4x – 3x3 + 5x-2
10 – 5y2
For each of the following;
a)
Determine if the expression is a polynomial (yes or no). If it is not a polynomial, explain why.
b)
If it is a polynomial, rewrite it in descending order (as specified)
c)
If it is a polynomial, state what type of polynomial it is (monomial, binomial, trinomial, polynomial).
1. 5 – 3x + x2
2. 4x – 3x3 + 5x-2
3. 10 – 5y2
4. 13xy-3
5. 5-1
6. 4x2y + 13 – 2x3y2 + 4x, descending order in terms of x
7. x5y2

Answer 3

something like \(\large x^2 + 3x + 10\) is a polynomial because each term with variables has exponents over the variables that are positive whole numbers

something like \(\large x^{-2}+5\) is NOT a polynomial because the exponent of -2 is NOT a positive number

something like \(\large x^{1.7}+3x\) is NOT a polynomial because the exponent of 1.7 is NOT a whole number

Answer 4

Also, if you have square roots over variables, then it's NOT a polynomial

If you are dividing by a variable (or variable expression), then it's NOT a polynomial

Answer 5

And can you give me an example of monomial, binomial, and trinomial.

Answer 6

Monomial: It means "one term" so things like 2x, 10abc, or -17z are all monomials. There are NO plus signs in monomials

Answer 7

Binomial: This means "two terms" (bi = two, nomial = name). Things like 2x + 3y and 10a + 11c are binomials. Notice how there are plus signs now. The plus signs separate the terms. If you have something like 12x - 3y you can rewrite it as 12x + (-3y) and notice how the plus sign shows up now separating the terms.

Answer 8

Trinomial: Three terms

Examples:

x^2 + 3x + 10
a^2 + 2ab + b^2

Answer 9

Polynomial: A monomial, a binomial, trinomial are all polynomials. Poly means "many" but even a monomial is a polynomial. A polynomial can have more than 3 terms. It can have 4, 5, 6, ... terms. There are no limits.

Examples

x^2 + 10x + 5
3x + 10y
a^2 + b^2 + c^2 + d^2
x + y + z + w + t + u

Answer 10

Also, with monomials, you can raise a variable or a product of variables to powers of POSITIVE WHOLE NUMBERS.

so you can start with x and bump it up to x^3 and it's a polynomial. But if you take x and change it to x^1.2, then it's no longer a polynomial.

So effectively a polynomial is defined to be a sum of monomials where each exponent is a positive whole number.

Answer 11

Thank you !

Answer 12

you're welcome

Answer 13

If you're curious, here's a link that has examples

http://www.mathsisfun.com/definitions/monomial.html