Determine whether the expression is a polynomial, if it is state how many terms and variables the polynomial contains. then state the degree

7x^2+3x+3

The given expression, 7x^2 + 3x + 3, is a polynomial.

It contains 3 terms: 7x^2, 3x, and 3.

It also contains 1 variable, which is x.

To determine the degree of the polynomial, we consider the highest exponent of the variable x. In this case, the highest exponent is 2, so the degree of the polynomial is 2.

To determine whether the expression 7x^2+3x+3 is a polynomial, let's break it down and analyze it.

A polynomial is an algebraic expression with one or more terms where each term consists of a coefficient multiplied by a variable raised to a non-negative integer exponent. In this case, we have three terms: 7x^2, 3x, and 3.

Each term consists of a coefficient multiplied by a variable raised to a non-negative integer exponent. The coefficients in this expression are 7, 3, and 3. The variable is x, and its exponents are 2, 1, and 0 (since x^0 is equivalent to 1).

Since all the terms in the expression fulfill the conditions of a polynomial, we can confirm that 7x^2+3x+3 is indeed a polynomial.

Now, let's determine the number of terms and variables the polynomial contains:

Number of terms: The polynomial has three terms: 7x^2, 3x, and 3.

Number of variables: The polynomial contains one variable, which is x.

Finally, let's find the degree of the polynomial:

Degree: The degree of a polynomial is the highest exponent of the variable in any of its terms. In this case, the highest exponent is 2. Thus, the degree of the polynomial 7x^2+3x+3 is 2.

There are 3 terms, so it is a polynomial. The only variable is x. The highest power of x is x^2 - the degree is 2.