Can someone please help

P

Polonium 84

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I have the following problem:
[math]2t^2 + 5t + 2.[/math]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: [math](2t+1)(t+2)[/math], where do I go from there? I absolutely do not know.
.
 
Polonium 84 said:
I have the following problem:
[math]2t^2 + 5t + 2.[/math]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: [math](2t+1)(t+2)[/math], where do I go from there? I absolutely do not know.
.
Click to expand...
Prime numbers can only be factorized into 1 and the number itself.
 
Polonium 84 said:
I have the following problem: [imath]2t^2 + 5t + 2.[/imath]
t is a positive whole number explain why this expression can never have a value that is a prime number.
.
Click to expand...
Other than [imath]2[/imath], are there any other even prime numbers?
 
Polonium 84 said:
I have the following problem:
[imath]2t^2 + 5t + 2.[/imath]
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: [imath](2t+1)(t+2)[/imath], where do I go from there? I absolutely do not know.
.
Click to expand...
If the value of [imath]2t^2 + 5t + 2[/imath] is a prime number, then [imath](2t+1)(t+2)[/imath], 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, [imath]2t+1[/imath] and [imath]t+2[/imath], be 1, given that t is a positive whole number?
 
Polonium 84 said:
I have the following problem:
[math]2t^2 + 5t + 2.[/math]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: [math](2t+1)(t+2)[/math], where do I go from there? I absolutely do not know.
.
Click to expand...
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.

[math]2t^2 + 5t + 2 = (2t + 1)(t + 2).[/math]
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.
 
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