Algebra II : Other Factorials

Study concepts, example questions & explanations for Algebra II

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Example Questions

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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 #92 : Factorials

Try without a calculator:

Which is true about  ?

Possible Answers:

 is an undefined quantity

Cannot be determined

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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