Precalculus : Algebra of Functions
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Example Questions
Example Question #1 : Algebra Of Functions
Simplify the following expression:
When multiplying polynomials, add their exponents.
Example Question #1 : Algebra Of Functions
Simplify this polynomial:
When dividing polynomials, you must subtract corresponding exponents.
Thus, our answer is
Example Question #2 : Algebra Of Functions
Simplify the following:
When dividing, we must subtract the exponents.
Thus, our answer is 
Example Question #1 : Algebra Of Functions
Fully expand the expression:
None of the other answers
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
None of the other answers
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:
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 
We now have
Example Question #4 : Add, Subtract, Multiply, And Divide Functions
Simplify the expression:
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 
We begin by factoring 
Now, When we look at 
We can take out 
Example Question #6 : Add, Subtract, Multiply, And Divide Functions
If 
First, we must determine what 
Next we simply subtract this from 
Finally, combining our terms gives us 
Example Question #7 : Add, Subtract, Multiply, And Divide Functions
Fully expand the expression:
Correct answer not listed
In order to fully expand the expression 
Then, using the FOIL(First, Outer, Inner, Last) Method of Multiplication, we expand the expression to:
First:
Outer:
Inner:
Last:
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