Q&A for How to Find the Degree of a Polynomial

In the case of a polynomial with only one variable (such as 2x³ + 5x² - 4x +3, where x is the only variable),the degree is the same as the highest exponent appearing in the polynomial (in this case 3). In the case of a polynomial with more than one variable, the degree is found by looking at each monomial within the polynomial, adding together all the exponents within a monomial, and choosing the largest sum of exponents. That sum is the degree of the polynomial. For example, in the expression 2x²y³ + 4xy² - 3xy, the first monomial has an exponent total of 5 (2+3), which is the largest exponent total in the polynomial, so that's the degree of the polynomial.

1 / (x^4) is equivalent to x^(-4). So the highest (most positive) exponent in the polynomial is 2, meaning that 2 is the degree of the polynomial.

Combine the exponents found within a given monomial as you would if all the exponents were positive, but you would subtract the negative exponents.

The multi-degree of a polynomial is the sum of the degrees of all the variables of any one term.

The degree is the same as the highest exponent appearing in the polynomial. Coefficients have a degree of 1.

When no exponent is shown, you can assume the highest exponent in the expression is 1. Therefore, the degree of this monomial is 1.

The degree is the same as the highest exponent appearing in the final product, so you just multiply the two factors and you'll wind up with x³ as one of the terms in the product. That's the highest exponent in the product, so 3 is the degree of the polynomial.

One. The term 3x is understood to have an exponent of 1.

The degree is 3.

A proper fraction is one whose numerator is less than its denominator. An improper fraction is one whose numerator is equal to or greater than its denominator.

1 is the degree of -10 because there is only one term and its power is 1, so the degree will be 1.

Yes. The expression can be simplified to 2x -1, which is a binomial. A binomial is a polynomial.

Technically it has no degree, because there's no variable. 8 is a monomial which can be expressed as 8^1 (8 to the power of 1), so you could think of the degree as 1.

Each term in the polynomial has an exponent of 1, so 1 is the degree of the polynomial. (Technically each constant and each variable in the whole equation carries an exponent of 1.)

You use the largest exponent when you want to discover the degree of a polynomial. You add exponents when you are multiplying two (or more) numbers of the same base -- for example, (x^3)(x^4) = x^(3+4) = x^7.

No, it's a monomial. A polynomial consists of more than one monomial separated from each other by a plus or minus sign.

8/x can be written as (8^1)[x^(-1)]. The highest (most positive) exponent is 1, so 1 is the degree of the expression.

The highest exponent is 5, so the degree of the polynomial is 5.

If there are no other terms with a higher exponent, the degree is 3.

The degree is 5 because that's the highest power (or exponent) in this polynomial.

That's not a polynomial. However, -1 does have a degree. Any term without an exponent actually has an "understood" exponent of 1. Therefore, -1 has a degree of 1.

The degree is 1. Any variable not showing an exponent is understood to have an exponent of 1.

When the multiplication is performed, there will be an x³ in the product, and that will be the highest exponent, so the polynomial's degree is 3.

25.

It doesn't matter. You still look for the highest power (or exponent) in the polynomial. For instance, the degree of the polynomial 6x^2 + 9x - 3 is 2, because 2 is the highest exponent in this polynomial.

The degree is 1. The first term has the largest exponent: 1.

3, because it is the highest power (or exponent) in this polynomial.

When a variable has no exponent, it actually has an "understood" exponent of 1. So that polynomial's degree is 1.

6, because it is the highest power (or exponent) in this polynomial.

The degree is 1. The only variable, r, has no exponent, which means it has an "understood" exponent of 1.