What does the symbol "!" mean in math terms?

Question

OKay im trying to do a calculus problem and it says to find the fourth derivative of (2 + 3x)^4 and i got the answer to be 1944. But these are the choices...

A)0
B)4!(3)
C)4!(3^4)
D)4!(3^5)
E)4!(2+3x)

Answer 1

In mathematics, the factorial of a non-negative integer n is the product of all positive integers less than or equal to n.

Combinatorics is, loosely, the science of counting. This is the area of mathematics in which we study families of sets (usually finite) with certain characteristic arrangements of their elements or subsets, and ask what combinations are possible, and how many there are.

This includes numerous quite elementary topics, such as enumerating all possible permutations or combinations of a finite set. Consequently, it is difficult to mention in this page all the topics with which a person new to combinatorics might come into contact. Moreover, because of the approachable nature of the subject, combinatorics is often presented with other fields (elementary probability, elementary number theory, and so on) to the exclusion of the more significant aspects of the subject.

factorial

The factorial, symbolized by an exclamation mark (!), is a quantity defined for all integers greater than or equal to 0.
For an integer n greater than or equal to 1, the factorial is the product of all integers less than or equal to n but greater than or equal to 1. The factorial value of 0 is defined as equal to 1. The factorial values for negative integers are not defined.

Mathematically, the formula for the factorial is as follows. If n is an integer greater than or equal to 1, then

n! = n(n - 1)(n - 2)(n - 3) ... (3)(2)(1)

If p = 0, then p! = 1 by convention.

The factorial is of interest to number theorists. It often arises in probability calculations, particularly those involving combinations and permutations. The factorial also arises occasionally in calculus and physics.

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Answer 2

It's pronounced "factorial", and it means take the product of the integer and all the positive integers leading up to it. So for example, 4! = 4 * 3 * 2 * 1 = 24. 0! is defined as 1 for certain exceptional reasons.

Notice that if you were to expand (2 + 3x)^4, the highest ordered term would be an x^4 term, so after taking 4 derivatives everything else would go to zero. In fact, the last term of this expansion should be (3x)^4, or (3^4)(x^4). You can see why the derivative would give you (4*3*2*1)(3^4)(x^0).

Answer 3

! means factorial.
4! = 1 x 2 x 3 x 4
7! = 1 x 2 x 3 x 4 x 5 x 6 x 7

C)4!(3^4) =
1 x 2 x 3 x 4 x 81 = 1944

Answer 4

The symbol "!" is a permutation symbol. Permutation is basically this: x(x-1)(x-2)...(2)(1)

So in the case of four, it would be: 4!= 4x3x2x1= 24
Other examples are 3!= 3x2x1= 6
2!= 2x1 =2
You can do it with most numbers (I'm not sure about 0 and negative numbers).

So, in the case of your problem, you can take 4!, and divide it into 1944, which will give you 81, which just happens to be 3^4. So your answer would be C: 4!(3^4)

Answer 5

The English word is "factorial". If you were multiplying
4 X 3 X 2 x 1, you could write that as 4!

Answer 6

! is the factorial symbol. n! means to multiply together all the integers from 1 to n.

so 4! means 4*3*2*1 = 24

Answer 7

The Power of 2 or Squared like 3^2=9 it's just the number multiplied by itself

Answer 8

! means that you have to multiply all the interger numbers from 1 up to the number that it says i.e. 4!= 1*2*3*4=24