Algebra II : Algebra II
Study concepts, example questions & explanations for Algebra II
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Example Questions
Example Question #12 : Factorials
Divide:
Write out the terms for the factorial.
Cancel out the common numbers in the numerator and denominator.
The answer is 
Example Question #13 : Factorials
Multiply:
To evaluate the product of these factorials, we will need to expand the factorials.
Multiply all the values.
The answer is:
Example Question #11 : Multiplying And Dividing Factorials
Divide:
Expand the factorials in the numerator and denominator.
The terms 1, 2, 3, and 4 can be eliminated from the numerator and denominator. The simplification becomes:
Example Question #11 : Factorials
Solve:
Evaluate the factorials first.
Substitute the values back into the expression.
Simplify the numerator.
Example Question #16 : Factorials
Solve the factorial:
Evaluate each factorial inside the parentheses.
Zero factorial is equal to 
The answer is 
Example Question #11 : Factorials
Simplify the following factorial:
Simplify the following factorial:
To solve this, we need to understand factorials. Factorials are denoted by a number followed by the ! sign. What a factorial is, is a given number multiplied by each positive integer leading up to the given number. Stated differently...
So what we have above is really:
Now, because numbers 1 through 14 are in the numerator and the denominator, they will cancel and we will be left with:
Example Question #18 : Factorials
Find the value of
If you were to write out the factorial problem above it would look like:
The only numbers that do not cancel out in the equation are the 
Example Question #21 : Factorials
Simplify the following:
To simplify the expression involving factorials, we must remember what a factorial is:
For our factorial expression, we can write out some of the terms of the numerator's factorial and we will be able to simplify from there:
As you can see, n! remains on top and bottom after writing out the first three terms of the numerator's factorial. There is no need to expand any further once we have the same factorial on top and bottom. They cancel, and we get our final answer.
Example Question #22 : Factorials
Simplify (leave as a product of binomials):
To simplify the expression, knowing that a factorial is, for example
will make it far easier.
Keeping this in mind, we can rewrite the given expression as
which simplifies to
after canceling like terms.
(One does not need to write out all terms of a factorial, rather as many in front that will leave something that cancels with another factorial are the most we usually need!)
Example Question #23 : Factorials
Simplify:
To simplify, remember that a factorial simply means we take the given term and subtract one unit from it successively until we reach 1, and multiply all the terms together:
Rewriting our given expression, we get:
Notice how we only expanded the factorials as much as we needed to in order to cancel things:
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