Question

Is the expression 3x^2-5x^3 a Polynomial? If yes, what is the degree?

Answer 1

Answer: The answer is: it is a fifth degree binomial or 'quintic binomial'.

Step-by-step explanation:

Is the expression 3x^2-5x^3 a polynomial?

So, we have to know what polynomial means. A polynomial is... "an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables."

So let's take a look at this expression.

Does it consist of variables and coefficients? YES

Does it only involve operations of addition, subtraction, multiplication, and non-negative integer exponents of variables? YES

Therefore, it is a polynomial.

Now, we have to figure out what degree this polynomial is.

The degree of the polynomial is the degree of the monomial with the largest degree.

So the largest degree would be the 3rd degree, because it is, of course, the largest out of the two powers listed.

And also, keep in mind that this is a binomial (made up of two monomials).

Therefore, it is a fifth degree binomial or 'quintic binomial'.