can anyone explain prime trinomials and give me an example of 1 that can't be solved?

Question

zepdrix · Answer

You're familiar with `prime numbers`, yes?
A number is prime if it has no other factors besides 1 and itself.
Example: $\large\rm 5=1\cdot5$

We do the same with polynomials.
A polynomial is a `prime trinomial` if it can not be broken down into factors besides 1 and itself.
Example: $\large\rm x^2+x-1\quad=\quad1\cdot(x^2+x-1)$

zepdrix · Answer

There are a lot of prime trinomials.
Take for example,

$\large\rm x^2+6x+8$
This is NOT prime,
it factors into $\large\rm (x+4)(x+2)$

Alternatively
$\large\rm x^2+6x+7$ is prime.
$\large\rm x^2+6x+6$ is prime.
$\large\rm x^2+6x+4$ is prime.

zepdrix · Answer

Do you understand how factoring works? :o
If not, prime trinomials might be a lil confusing.