Algebra II : Polynomial Functions

Study concepts, example questions & explanations for Algebra II

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Example Questions

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Example Question #1 : Polynomial Functions

Give the degree of the polynomial.

Possible Answers:

Correct answer:

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 #1 : Polynomial Functions

What is the degree of the polynomial?

Possible Answers:

Correct answer:

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 #1 : How To Find The Degree Of A Polynomial

What is the degree of the polynomial?

 

Possible Answers:

Correct answer:

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 #3 : Polynomial Functions

Let , and . What is ?

Possible Answers:

Correct answer:

Explanation:

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

and

Example Question #4 : Polynomial Functions

Let , and . What is ?

Possible Answers:

Correct answer:

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 #5 : Polynomial Functions

Evaluate  if  and 

Possible Answers:

Correct answer:

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 #6 : Polynomial Functions

Evaluate  if  and

Possible Answers:

Correct answer:

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 #7 : Polynomial Functions

 and .

Determine .

Possible Answers:

Correct answer:

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 #8 : Polynomial Functions

Which of the following depicts an equation in standard form?

Possible Answers:

None of the other answers are correct.

Correct answer:

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 #538 : Functions And Graphs

 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.

 

Indentify the expression below which is not a polynomial:

Possible Answers:

2

1

4

3

5

Correct answer:

5

Explanation:

Expression 5 has the term , which violates the definition of a polynomial.  The exponent must be a whole number.

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