## ahoymewmew 3 years ago the trinomial 10x2 + 11x + 3 is prime?

1. sauravshakya

can u factor 10x2 + 11x + 3

2. siddhantsharan

I dont get it. How can a trinomial be a prime?

3. ahoymewmew

@siddhantsharan its like a true or false answer, i guess its false.

4. sauravshakya

If u cannot factor it then it is prime

5. sauravshakya

And Yes it is prime as it cannot be factored

6. siddhantsharan

\[10x^2 + 5x + 6x +3 = 5x(2x+1) + 3(2x+1)=(5x+3)(2x+1)\] I guess what they are asking is whether it can ever YIELD a prime.

7. ahoymewmew

oh factors always confuse me i never seem to understand them. @sauravshakya & @siddhantsharan

8. siddhantsharan

In the sense for different value of x can the operation give a prime. If thats the case then, For a prime, one term must be 1. => Case 1. 2x + 1 = 1 => x = 0 In this case we get a three. Which is prime. So I dunno. The question is a bit ambigous I guess. As only numbers can be primes or composites. @sauravshakya It can be factored.

9. ahoymewmew

could you like help me how to factor something like this 4x2 + 24x + 11?

10. ahoymewmew

then it tells you which one of these is part of the factored answer. (2x + 1) (2x - 11) (2x + 6) prime.

11. siddhantsharan

Yeah. The trick is: Check the product of the constant term and the coefficient of x^2. Here it is 44. Then think of such factors of 44 which add up to 24. Here they are 2 and 22. So now you write it as: \[4x^2 + 2x+22x+11=2x(2x+1)+11(2x+1) = (2x+11)(x+1)\]

12. ahoymewmew

so for something like 9x2 - 18xy + 5y2 you look at 9x^2 first and get 81 then think of factors of 81? @siddhantsharan

13. sauravshakya

Oh ya @siddhantsharan it can be factored... THUS,10x2 + 11x + 3 is not a prime

14. sauravshakya

Because prime numbers cannot be factored

15. sauravshakya

Here 10x2 + 11x + 3 is a number

16. sauravshakya

And x is constant