### All SAT Math Resources

## Example Questions

### Example Question #1 : Polynomial Operations

Find the degree of the polynomial:

**Possible Answers:**

**Correct answer:**

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.

### Example Question #2 : Polynomial Operations

What is the degree of the polynomial ?

**Possible Answers:**

**Correct answer:**

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.

### Example Question #3 : Polynomial Operations

Find the degree of the following polynomial:

**Possible Answers:**

**Correct answer:**

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.

### Example Question #4 : Polynomial Operations

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

What is the degree of the following polynomial?

**Possible Answers:**

**Correct answer:**

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

### Example Question #5 : Polynomial Operations

What is the degree of this polynomial?

**Possible Answers:**

Degree 10

Degree 6

Degree 12

Degree 7

Degree 8

**Correct answer:**

Degree 8

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.

### Example Question #6 : Polynomial Operations

Find the degree of the following polynomial:

**Possible Answers:**

**Correct answer:**

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.