# Precalculus : Algebra of Functions

## Example Questions

### Example Question #1 : Algebra Of Functions

Simplify the following expression:

Possible Answers:

Correct answer:

Explanation:

When multiplying polynomials, add their exponents.

### Example Question #1 : Algebra Of Functions

Simplify this polynomial:

Possible Answers:

Correct answer:

Explanation:

When dividing polynomials, you must subtract corresponding exponents.

Thus, our answer is

.

### Example Question #2 : Algebra Of Functions

Simplify the following:

Possible Answers:

Correct answer:

Explanation:

When dividing, we must subtract the exponents.

Thus, our answer is  .

### Example Question #1 : Algebra Of Functions

Fully expand the expression:

Possible Answers:

None of the other answers

Correct answer:

Explanation:

The first step is to rewrite the expression:

Now that it is expanded, we can FOIL (First, Outer, Inner, Last) the expression:

First :

Outer:

Inner:

Last:

Now we can simply add up the values to get the expanded expression:

### Example Question #2 : Add, Subtract, Multiply, And Divide Functions

Evaluate

Possible Answers:

None of the other answers

Correct answer:

Explanation:

When adding two expressions, you can only combine terms that have the same variable in them.

In this question, we get:

Now we can add each of the results to get the final answer:

### Example Question #3 : Add, Subtract, Multiply, And Divide Functions

Simplify the following expression:

.

Possible Answers:

Correct answer:

Explanation:

First, we can start off by factoring out constants from the numerator and denominator.

The 9/3 simplifies to just a 3 in the numerator. Next, we factor the top numerator into , and simplify with the denominator.

We now have

### Example Question #4 : Add, Subtract, Multiply, And Divide Functions

Simplify the expression:

.

Possible Answers:

Correct answer:

Explanation:

First, distribute the -5 to each term in the second expression:

Next, combine all like terms

to end up with

.

### Example Question #5 : Add, Subtract, Multiply, And Divide Functions

If  and , what does  equal?

Possible Answers:

Correct answer:

Explanation:

We begin by factoring  and we get .

Now, When we look at  it will be .

We can take out  from the numerator and cancel out the denominator, leaving us with .

### Example Question #6 : Add, Subtract, Multiply, And Divide Functions

If  and , then what is  equal to?

Possible Answers:

Correct answer:

Explanation:

First, we must determine what  is equal to. We do this by distributing the 3 to every term inside the parentheses,.

Next we simply subtract this from , going one term at a time:

Finally, combining our terms gives us .

### Example Question #7 : Add, Subtract, Multiply, And Divide Functions

Fully expand the expression:

Possible Answers:

Correct answer not listed

Correct answer:

Explanation:

In order to fully expand the expression , let's first rewrite it as:

.

Then, using the FOIL(First, Outer, Inner, Last) Method of Multiplication, we expand the expression to:

First:

Outer:

Inner:

Last:

, which in turn