Question 404615
1. You are right it is prime. A quick way to tell if it is prime is to find the value of {{{b^2-4ac}}}. You may recognize this as the expression inside the square root in the Quadratic Formula. This is expression is called the discriminant. It can be used to determine the number and types of solutions to a quadratic equaiton. It can also be used to determine if the quadratic will factor.<br>
The value of your discriminant:
{{{(2)^2-4(2)(1)}}}
which simplifies as follows:
{{{4-4(2)(1)}}}
{{{4 - 8}}}
{{{-4}}}
If the discriminant is not a perfect square, then the quadratic expression will not factor. -4 is not a perfect square (4 is but not -4) so this verifies that the expression is prime.<br>
2. I solved this problem for someone else earlier today. <A HREF=http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.404639.html>Click here</A> to see it.