Can someone please help

[Polonium 84]

I have the following problem:
$$2t^2 + 5t + 2.$$t is a positive whole number explain why this expression can never have a value that is a prime number.
I have factorized it to give me: $$(2t+1)(t+2)$$, where do I go from there? I absolutely do not know.
.

 

[Deleted member 4993]

I have the following problem:
$$2t^2 + 5t + 2.$$t is a positive whole number explain why this expression can never have a value that is a prime number.
I have factorized it to give me: $$(2t+1)(t+2)$$, where do I go from there? I absolutely do not know.
.

Prime numbers can only be factorized into 1 and the number itself.

 

[pka]

I have the following problem: $2t^2 + 5t + 2.$
t is a positive whole number explain why this expression can never have a value that is a prime number.
.

Other than $2$, are there any other even prime numbers?

 

[Polonium 84]

Other than $2$, are there any other even prime numbers?

no sir however you have 5t

 

[Polonium 84]

Prime numbers can only be factorized into 1 and the number itself.

i don't get what you are saying how does effect the averall value of the expression.

 

[Deleted member 4993]

i don't get what you are saying how does effect the averall value of the expression.

You have factored the expression - which one of those could be equal to one ?

 

[Polonium 84]

You have factored the expression - which one of those could be equal to one ?

What do you mean by those? sorry for being a little slow in this topic I am not the best at it

 

[Deleted member 4993]

What do you mean by those? sorry for being a little slow in this topic I am not the best at it

You have the factors:

I have factorized it to give me: (2t+1)(t+2)

I mean those factors.

 

[eddy2017]

Other than $2$, are there any other even prime numbers?

 

[eddy2017]

sorry I was going to ask something but I'd better not.

 

[Dr.Peterson]

I have the following problem:
$2t^2 + 5t + 2.$
t is a positive whole number explain why this expression can never have a value that is a prime number.
I have factorized it to give me: $(2t+1)(t+2)$, where do I go from there? I absolutely do not know.
.

If the value of $2t^2 + 5t + 2$ is a prime number, then $(2t+1)(t+2)$, which is a product of two integers, has to be the product of 1 and another integer; otherwise it would be composite. For example a number that could be factored as 2*3 is composite.

So, can either of those factors, $2t+1$ and $t+2$, be 1, given that t is a positive whole number?

 

[JeffM]

I have the following problem:
$$2t^2 + 5t + 2.$$t is a positive whole number explain why this expression can never have a value that is a prime number.
I have factorized it to give me: $$(2t+1)(t+2)$$, where do I go from there? I absolutely do not know.
.

The DEFINITION of a prime number is an integer that is greater than 1 and has no positive integer factors other than 1 and itself.

$$2t^2 + 5t + 2 = (2t + 1)(t + 2).$$
Suppose 2t + 1 = 1, then t = 0. But by hypothesis, t is positive.

Suppose t + 2 = 1, then t = - 1. But by hypothesis, t is positive.

So, subject to the constraint on t, t^2 + 5t + 2 cannot meet the definition of a prime number.

This was the logic behind SK’s hint, and is just a different way to express Dr. P’s response. Choose whichever is most intuitive to you.