Algebra II : Factorials

Example Questions

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Example Question #91 : Factorials

Multiply:

Explanation:

Simplify all the terms in the parentheses first.

This indicates that:

Example Question #92 : Factorials

Evaluate:

None of the other choices gives the correct response.

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.

:

:

:

:

Example Question #93 : Factorials

Try without a calculator:

True or false:

False

True

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.

The inequality has no solution.

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?

None of these

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  ?

Cannot be determined

is an undefined quantity

Explanation:

is considered to be equal to one by definition.

Example Question #97 : Factorials

Try without a calculator:

Calculate:

Cannot be determined

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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