Algebra II : Factorials

Study concepts, example questions & explanations for Algebra II

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Example Questions

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Example Question #1 : Factorials

What is the value of .

Possible Answers:

None of the other answers.

Correct answer:

Explanation:

When evaluating a factorial, you multiply the original number by each integer less than it, stopping at 1.

For this problem, this means that

 .

Then adding 3, we get the answer 123

Example Question #1 : Factorials

Which of the following best represents the approximate value of ?

Possible Answers:

Correct answer:

Explanation:

The value of  is defined as .

To find , simply cube the decimal number.

The closest value of this number is:  

Example Question #1 : Multiplying And Dividing Factorials

Stewie has   marbles in a bag. How many marbles does Stewie have? 

Possible Answers:

Correct answer:

Explanation:

Simplifying this equation we notice that the 3's, 2's, and 1's cancel so

Alternative Solution

Example Question #1 : Multiplying And Dividing Factorials

Which of the following is NOT the same as ?

Possible Answers:

Correct answer:

Explanation:

The  cancels out all of  except for the parts higher than 4, this leaves a 6 and a 5 left to multilpy 

Example Question #2 : Multiplying And Dividing Factorials

Simplify the following expression:

Possible Answers:

Correct answer:

Explanation:

Recall that .

Likewise, .

Thus, the expression  can be simplified in two parts:

 

and

The product of these two expressions is the final answer: 

Example Question #4 : Factorials

Possible Answers:

Correct answer:

Explanation:

To simplify this, just write out each factorial:

Example Question #2 : Multiplying And Dividing Factorials

Find the value of:

Possible Answers:

Correct answer:

Explanation:

The factorial sign (!) just tells us to multiply that number by every integer that leads up to it.  So,  can also be written as: 

To make this easier for ourselves, we can cancel out the numbers that appear on both the top and bottom:

Example Question #1 : Multiplying And Dividing Factorials

Which of the following is equivalent to ?

Possible Answers:

None of the other answers are correct.

Correct answer:

Explanation:

This is a factorial question. The formula for factorials is .

 

Example Question #5 : Factorials

Divide  by 

Possible Answers:

Correct answer:

Explanation:

A factorial is a number which is the product of itself and all integers before it. For example

In our case we are asked to divide  by . To do this we will set up the following:

We know that  can be rewritten as the product of itself and all integers before it or:

Substituting this equivalency in and simplifying the term, we get:

 

Example Question #2 : Multiplying And Dividing Factorials

If  is a postive integer, which of the following answer choices is a possible value for the expression.

Possible Answers:

Correct answer:

Explanation:

This expression of factorials reduces to (n+1)(n+2).  Therefore, the solution must be a number that multiplies to 2 consecutive integers.  Only 30 is a product of 2 consecutive integers.  

So n would have to be 4 in this problem.

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