How to find the degree of a polynomial

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SAT Math › How to find the degree of a polynomial

Questions 1 - 6
1

Find the degree of the polynomial:

Explanation

To find the degree of a polynomial we must find the largest exponent in the function.

The degree of the polynomial is 5, as the largest exponent of is 5 in the second term.

2

Find the degree of the following polynomial:

Explanation

When a polynomial has more than one variable, we need to find the degree by adding the exponents of each variable in each term.

Even though has a degree of 5, it is not the highest degree in the polynomial -

has a degree of 6 (with exponents 1, 2, and 3). Therefore, the degree of the polynomial is 6.

3

Solve each problem and decide which is the best of the choices given.

What is the degree of the following polynomial?

Explanation

The degree is defined as the largest exponent in the polynomial. In this case, it is .

4

Find the degree of the following polynomial:

Explanation

The degree of a polynomial is the largest exponent on one of its variables (for a single variable), or the largest sum of exponents on variables in a single term (for multiple variables).

Here, the term with the largest exponent is , so the degree of the whole polynomial is 6.

5

What is the degree of this polynomial?

Degree 8

Degree 7

Degree 6

Degree 12

Degree 10

Explanation

When an exponent with a power is raised to another power, the value of the power are multiplied.

When multiplying exponents you add the powers together

The degree of a polynomial is the determined by the highest power. In this problem the highest power is 8.

6

What is the degree of the polynomial ?

Explanation

When a polynomial has more than one variable, we need to find the degree by adding the exponents of each variable in each term.

has a degree of 4 (since both exponents add up to 4), so the polynomial has a degree of 4 as this term has the highest degree.

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