Question

I have to factor this equation, which is a perfect square:

2p^2+4p+1

How do I do this?

Answer 1

This expression can be factorized, but not with rational coefficients, nor is it a perfect square.
The easiest way is to find the roots, either by completing the squares, or using the quadratic formula. I chose the latter, which gives as roots
-1 ±√2/2
So the expression factors as
(sqrt(2)p+sqrt(2)+1)*(sqrt(2)p+sqrt(2)-1);
or equivalently,
(p+1+sqrt(2)/2)(2p+2-sqrt(2))

Answer 2

Oh! Of course it isn't a perfect square, because of the 2, right?

Jeez do I ever hate trick questions. Thanks a lot. :) I was really stuck and now I know why! Haha!

- <3

Answer 3

In the quadratic formula, if the term inside the square-root sign, "b²-4ac" is not zero, it will not be a perfect square.
In this case, b²-4ac = 4²-4*2*1 = 8, so you can quickly tell that it won't be a perfect square.
Do check to see if you have copied the question correctly. :)