All Algebra II Resources
Example Questions
Example Question #1 : Factorials
What is the value of .
None of the other answers.
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 ?
The value of is defined as .
To find , simply cube the decimal number.
The closest value of this number is:
Example Question #1 : Factorials
Stewie has marbles in a bag. How many marbles does Stewie have?
Simplifying this equation we notice that the 3's, 2's, and 1's cancel so
Alternative Solution
Example Question #182 : Algebra Ii
Which of the following is NOT the same as ?
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 : Factorials
Simplify the following expression:
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 #1 : Multiplying And Dividing Factorials
To simplify this, just write out each factorial:
Example Question #1 : Multiplying And Dividing Factorials
Find the value of:
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 #4 : Factorials
Which of the following is equivalent to ?
None of the other answers are correct.
This is a factorial question. The formula for factorials is .
Example Question #2 : Factorials
Divide by
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 #1 : Factorials
If is a postive integer, which of the following answer choices is a possible value for the expression.
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.