Question

Provide an example of a prime polynomial and explain why it is defined as prime.

Please help...

Answer 1

let's say you had something like x^2 + 5x + 6

Answer 2

that's factorable because 2+3 = 5 and 2*3 = 6, so

x^2 + 5x + 6 = (x+2)(x+3)

based on these two facts

Answer 3

but if you change the last number to some prime number, then there's only one way to factor it: that number itself multiplied by 1

so if you changed the 6 to 17, then the middle number must be 17+1 = 18 or else you cannot factor

Answer 4

this means

x^2 + 5x + 17

cannot be factored, so it's prime

Answer 5

It's probably not cool to ask a question you can Google:

http://www.virtualnerd.com/algebra-2/polynomials/equations/factoring-strategies/prime-polynomial-definition