**Examples of prime polynomials include 2x ^{2}+14x+3 and x^{2}+x+1.** Prime numbers in mathematics refer to any numbers that have only one factor pair, the number and 1. A polynomial is considered prime if it cannot be factored into the standard linear form of (x+a)((x+b).

A given expression is a polynomial if it has more than one term. An example of a polynomial that can be factored would be x^{2}+4x+4. In this case, the polynomial can be factored to (x+2)(x+2). To factor a polynomial, first look for the greatest common factor and then either factor by grouping, factor as a difference or sum or two squares or cubes or factor as a product of two binomials.