is f(x)=4x^4+4x+2 irreducible?

Question

how do i go about figuring out if this is irreducible or not??? someone plz help!

Answer 1

If you mean that it factors into neat terms with integers, the answer is no. If you apply the quadratic formula, check the term b^2-4ac, where a, b are the coefficients of the x^2 and x terms and c is the constant. If it is zero, your roots are both b/2a. If it is a perfect square, you have a rational solution. If it is not a perfect square, you have an irrational solution. If the term is imaginary, you have an imaginary solution. I think this falls into the last group.