The expression [tex]2t^2 + 5t + 2[/tex] can never have a value that is a prime number. Can someone please explain in simple steps why this is? Thank you!

The given **expression **can be factored in the form (2t+1) and (t+2) so 2t² + 5t + 2 cannot be a prime number.
What are prime numbers?
A whole number greater than 1 that has no factor other than 1 and the number itself is called a prime number.
For examples ; 3,11,19 ... all these numbers can only be divided by 1 or the number itself so they are called prime .
Given an expression 2t² + 5t + 2 , it is said that t is positive whole number. So if t is a positive whole number then the **expression **can be written as another positive whole number.
Now the **expression **2t² + 5t + 2 can be factored into two smaller factors.
= 2t² + 5t + 2
= 2t² + 4t + t + 2
= 2t (t + 2 )+1 (t+2)
= (t+2) (2t+1)
If t is a positive whole number then t+2 is a whole number and 2t+1 is another positive whole number.
Hence, these two numbers are factors of 2t² + 5t + 2 . But a **prime **number does not have any factors. So 2t² + 5t + 2 is not a **prime **number.
To learn more about prime numbers visit:
brainly.com/question/4184435
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Answered by astha8579 | 2024-06-17

I would assume that the fact you have squared a number means it is devisable by it's square root and not just 1 and itself . That's a start I suppose

Answered by jordancable | 2024-06-24

The expression 2 t 2 + 5 t + 2 always results in an even number when factored as ( 2 t + 1 ) ( t + 2 ) . Since the only even prime number is 2 and the expression never equals 2, it can never yield a prime number. Therefore, for any positive integer t , the expression will always produce composite values, thus never being prime.
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Answered by astha8579 | 2024-10-12