# Algebra II : Polynomial Functions

## Example Questions

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### Example Question #1 : How To Find The Degree Of A Polynomial

Give the degree of the polynomial.

Explanation:

The degree of an individual term of a polynomial is the exponent of its variable; the exponents of the terms of this polynomial are, in order, 5, 4, 2, and 7.

The degree of the polynomial is the highest degree of any of the terms; in this case, it is 7.

### Example Question #2 : How To Find The Degree Of A Polynomial

What is the degree of the polynomial?

Explanation:

To find the degree of the polynomial, you first have to identify each term [term is for example ], so to find the degree of each term you add the exponents.

EX:   - Degree of 3

Highest degree is

### Example Question #3 : How To Find The Degree Of A Polynomial

What is the degree of the polynomial?

Explanation:

To find the degree of the polynomial, add up the exponents of each term and select the highest sum.

12x2y3: 2 + 3 = 5

6xy4z: 1 + 4 + 1 = 6

2xz: 1 + 1 = 2

The degree is therefore 6.

### Example Question #1 : Polynomial Functions

Let , and . What is ?

Explanation:

When solving functions within functions, we begin with the innermost function and work our way outwards. Therefore:

and

### Example Question #2 : Polynomial Functions

Let , and . What is ?

Explanation:

This problem relies on our knowledge of a radical expression  equal to . The functions are subbed into one another in order from most inner to most outer function.

and

### Example Question #3 : Polynomial Functions

Evaluate  if  and

Explanation:

In problems with functions within one another, we must first solve the innermost function and then proceed outwards. Therefore, the first step is solving  :

Now, we must find the values of :

Because our x term is squared in this function, both values end up being the same. Therefore, 59 is our final answer.

### Example Question #4 : Polynomial Functions

Evaluate  if  and

Explanation:

Beginning with the innermost function, we must first solve for :

We then take this value and plug it into :

This has no value in the real number plane, and the answer is therefore undefined.

### Example Question #5 : Polynomial Functions

and .

Determine .

Explanation:

Substituting -x into f(x).  This has no effect on the 1st and 3rd terms.  This changes the sign of the middle term.

### Example Question #4 : How To Find The Degree Of A Polynomial

Which of the following depicts an equation in standard form?

None of the other answers are correct.

Explanation:

A polynomial in standard form is written in descending order of the power. The highest power should be first, and the lowest power should be last.

The answer has the powers decreasing from four, to two, to one, to zero.

### Example Question #77 : How To Find The Degree Of A Polynomial

A polynomial consists of one or more terms where each tem has a coefficient and one or more variables raised to a whole number exponent.  A term with an exponent of 0 is a constant.

Identify the expression below that is not a polynomial:

5

4

3

2

1