Which trinomials are prime?

Choose all answers that are correct.

x^2 – 8x + 2

x^2 + 4x + 5

x^2 + 11x + 18

x^2 – 3x – 2

is prime

Step-by-step explanation:

Prime Trinomials

A given trinomial is prime if it cannot be factored. The general expression for a trinomial is

Another useful expression is

where x1 and x2 are the zeroes of the trinomial.

The zeroes can be computed by using the known formula

The trinomial has two zeroes if the root can be found as a real number, that is if d is positive or zero, where

Let's test the four options

Since d is positive, the trinomial can be factored and therefore is not prime

Since d is negative, the trinomial is prime

Since d is positive, the trinomial can be factored and therefore is not prime

Since d is positive, the trinomial can be factored and therefore is not prime

step-by-step explanation: