SOLUTION: Hi, can you please help me?? 1. I need to factor this problem first: 2x^2+2x+1 ---> I think it is prime, can you tell if I'm correct, please? 2. I also need to solve th

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hi, can you please help me?? 1. I need to factor this problem first: 2x^2+2x+1 ---> I think it is prime, can you tell if I'm correct, please? 2. I also need to solve th      Log On


   

Question 404615: Hi, can you please help me??
1. I need to factor this problem first:
2x^2+2x+1 ---> I think it is prime, can you tell if I'm correct, please?
2. I also need to solve the following equation:
8x^3+1=0 ---> I tried doing the sum of two cubes, and ended up with x= -1/2, 1/2, and 1/2...can you please tell me if I'm doing it wrong, and show me how to do it correctly?
Thank you so much!
Answer by jsmallt9(3759) About Me  (Show Source):
You can put this solution on YOUR website!
1. You are right it is prime. A quick way to tell if it is prime is to find the value of b%5E2-4ac. 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.

The value of your discriminant:
%282%29%5E2-4%282%29%281%29
which simplifies as follows:
4-4%282%29%281%29
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.

2. I solved this problem for someone else earlier today. Click here to see it.