Is 2x+3 prime? explain.?

It depends on what the value of x is.

When x = 2:
2x + 3 = 2(2) + 3 = 7
2x + 3 is prime when x = 2.

When x = 6:
2x + 3 = 2(6) + 3 = 15 = 3 × 5
2x + 3 is not prime when x = 6

In terms of polynomials, yes.  It's prime.

It means it can't be factored.

Like a prime number:  13

It can't be factored.  But composite numbers can:

6 = 3 * 2

So your polynomial expression of (2x + 3) is prime since you cannot factor it.

If it was:

2x² + 3x

then it would not be as you can factor out the x:

x(2x + 3)

Yes, because 2 and 3 is only divisible by number 1 and itself.

Whether 2x+3 is a prime, it is uncertain because
x can vary. if x is given 3, then 2x+3=9 is not a prime;
if x is given 2, then 2x+3=7 is a prime.

No; If x = 3 you get 9. That number isnt prime.

Since ;x can be any Real number:
x = 1.5
2(1.5) + 3 = 6
So not prime.

No, 2x + 3 is not always prime.

Apart from 2, all prime numbers are odd and so can be expressed as
2x + 3, where x is {0, 1, 2, 3, 4, 5, ....etc)
However the reverse is not always true.
Some odd numbers are prime, such as 3, 5, 7, 11, 13, 17, 19, 23, ...
But other odd numbers are composite, (can be factored), such as 9, 15, 21, 25
In summary, 2x + 3 is not always prime

Is 2x + 3 prime ?
5, 7, 9, 11, 13, 17, 19, 21, .....
No, 2x + 3 is not always prime.

Not necessarily, no.  I offer X=6 so the expression yields 15, as proof of lack of universal truth.  Bascially, any X where X is divisible by 3 would have that expression yield a prime number.  The solution to the expression would be divisible by 3 (could be re-written as 3(2y+1) where y is an integer that is equal to x/3.

2x+3 is NOT a prime number, its an expression.

However, depending on the value of x, the expression 2x+3 can be a prime (number). In fact, there is a one-to-one correspondence of 2x+3 and the prime numbers. That is, all primes (except for 2) can be written as 2x+3. For instance, given any prime P, let

2x+3 = P. Since P is odd then P-3 is even and thus can be divided by two.
That is, let x = (P-3)/2, and is always an integer. 

However, the converse is not true: 2x+3 is not always a prime. 
Once more, all primes can be written as 2x+3. 

depends on x's value
If x = 6, 2(6) + 3 = 15 which is composite.
If x = 0, 2(0) + 3 = 3 which is prime.

As pingshek said, the expression may be prime depending on the value of x.

You can make a little table for the values of x that make it prime or not prime

When x is ..... the expression is
------------------  -----------------------------
1 . . . . . . . . . . . . Prime
2 . . . . . . . . . . . . Prime
3 . . . . . . . . . . . . Not prime
4 . . . . . . . . . . . . Prime
5 . . . . . . . . . . . . Prime
6 . . . . . . . . . . . . Not prime
7 . . . . . . . . . . . . Prime
8 . . . . . . . . . . . . Prime
9 . . . . . . . . . . . . Not prime
10 . . . . . . . . . . . Prime
11 . . . . . . . . . . . Not prime
12 . . . . . . . . . .. .Not prime

This chart shows you that when x = 3 or the multiples of 3, the expression is not prime.

The general expression is
Let 3n represent "any multiple 3"
When x = any multiple of 3 = 3n
2(3n) + 3
6n + 3

No matter what the value of n is (no matter what multiple of 3 you are using),
6n + 3 can always be factored as
3(2n + 1)
So when x = any multiple of 3, the result can always be factored by 3
---------------------------------

The other instance is when x = 11

When x = 11, then the expression is
2(11) + 3
22 + 3
25
(5)(5)

Unlike the multiples of 3, for the multiples of 11, the expression is sometimes "prime" and sometimes "not prime"
When x = 22
2(22) + 3
44 + 3
47

But when x = 33
2(33) + 3
66 + 3
69
3(23)

When x = 44
2(44) + 3
88 + 3
91

So it looks like the expression is not prime for the ODD multiples of 11, in addition to ALL the multiples of 3

Oops!
I just tried another odd multiple of 11 -- namely 5(11), and the result was a prime number

When x = 55
2(55) + 3
110 +3
113