Algebra II : Factorials

Study concepts, example questions & explanations for Algebra II

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Example Questions

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Example Question #91 : Factorials

Multiply:  

Possible Answers:

Correct answer:

Explanation:

Simplify all the terms in the parentheses first.

This indicates that:

The answer is:  

Example Question #92 : Factorials

Evaluate:

Possible Answers:

None of the other choices gives the correct response.

Correct answer:

Explanation:

 is equal to the sum of the expressions formed by substituting 1, 2, 3 and 4, in turn, for  in the expression  , as follows:

 - or  factorial - is defined to be the product of the integers from 1 to  . Therefore, each term can be calculated by multiplying the integers from 1 to , then taking the reciprocal of the result.

:

 

:

 

:

 

:

 

Add the terms:

Example Question #93 : Factorials

Try without a calculator:

True or false: 

Possible Answers:

False

True

Correct answer:

False

Explanation:

 - or  factorial - is defined to be the product of the integers from 1 to . Therefore, 

Since ,

and 

 is a false statement.

Example Question #94 : Factorials

Try without a calculator.

Give the value of  that makes this three-part inequality true.

Possible Answers:

The inequality has no solution.

Correct answer:

Explanation:

Given a nonnegative integer  - or  factorial - is defined to be the product of the integers from 1 to . After some exploration, multiplying 1 by 2, the result by 3, that result by 4, and so forth, we find that

Multiplying by 8, we find that

Multiplying by 9, we find that

Therefore,

Since only integers may have factorial values, it follows that the only value of  that makes the inequality true is .

Example Question #95 : Factorials

Try without a calculator:

 is equal to which expression?

Possible Answers:

None of these

Correct answer:

Explanation:

 - or  factorial - is defined to be the product of the integers from 1 to . Therefore, 

and 

,

the correct response.

Example Question #96 : Factorials

Try without a calculator:

Which is true about  ?

Possible Answers:

Cannot be determined

 is an undefined quantity

Correct answer:

Explanation:

 is considered to be equal to one by definition.

Example Question #97 : Factorials

Try without a calculator:

Calculate:

Possible Answers:

Cannot be determined

Correct answer:

Explanation:

 - or  factorial - is defined to be the product of the integers from 1 to . Therefore, 

Therefore, 

Since

,

it follows that 720 is the correct response. 

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