### All PSAT Math Resources

## Example Questions

### Example Question #1 : Polynomials

Give the degree of the polynomial

**Possible Answers:**

**Correct answer:**

The polynomial has one term, so its degree is the sum of the exponents of the variables:

### Example Question #1 : Polynomials

Give the degree of the polynomial

**Possible Answers:**

**Correct answer:**

The degree of a polynomial in more than one variable is the greatest degree of any of the terms; the degree of a term is the sum of the exponents. The degrees of the terms in the given polynomial are:

The degree of the polynomial is the greatest of these degrees, 100.

### Example Question #1 : Polynomials

Give the degree of the polynomial

**Possible Answers:**

**Correct answer:**

The degree of a polynomial in one variable is the greatest exponent of any of the powers of the variable. The terms have as their exponents, in order, 44, 20, 10, and 100; the greatest of these is 100, which is the degree.

### Example Question #4 : Polynomial Operations

Give the degree of the polynomial

**Possible Answers:**

**Correct answer:**

The degree of a polynomial in one variable is the greatest exponent of any of the powers of the variable. The terms have as their exponents, in order, 10, 20, 30, and 40; 40 is the greatest of them and is the degree of the polynomial.

### Example Question #5 : Polynomial Operations

Which of these polynomials has the greatest degree?

**Possible Answers:**

All of the polynomials given in the other responses have the same degree.

**Correct answer:**

All of the polynomials given in the other responses have the same degree.

The degree of a polynomial is the highest degree of any term; the degree of a term is the exponent of its variable or the sum of the exponents of its variables, with unwritten exponents being equal to 1. For each term in a polynomial, write the exponent or add the exponents; the greatest number is its degree. We do this with all four choices:

:

A constant term has degree 0.

The degree of this polynomial is 5.

The degree of this polynomial is 5.

The degree of this polynomial is 5.

The degree of this polynomial is 5.

All four polynomials have the same degree.

### Example Question #6 : Polynomial Operations

Which of the following monomials has degree 999?

**Possible Answers:**

None of the other responses is correct.

**Correct answer:**

The degree of a monomial term is the sum of the exponents of its variables, with the default being 1.

For each monomial, this sum - and the degree - is as follows:

:

:

: (note - 999 is the *coefficient*)

:

is the correct choice.

### Example Question #7 : Polynomial Operations

Find the degree of the polynomial

**Possible Answers:**

None of the other answers

**Correct answer:**

The degree of the polynomial is the largest degree of any one of it's individual terms.

The degree of is

The degree of is

The degree of is

The degree of is

The degree of is

is the largest degree of any one of the terms of the polynomial, and so the degree of the polynomial is .