Help With Factoring

[StanTheMan]

I came across this problem on a math worksheet while I was getting rid of my useless school stuff from the previous year, and noticed this problem that I hadn't done. It ask me to factor (4x^2)+49 and I have no idea how to do it. I know the answer is (2x+7i)(2x-7i) because I looked it up on Wolframalpha, but I have no idea how to actually do the problem.

[mark79]

The factors of 49 are 1, 7, and 49.
The i is necessary because the 49 is positive. In order for the x^1 part of the polynomial to equal 0, the 7*2x factors must cancel and so the signs must be opposite. But opposite signs without i would result in -49 as the constant. Multiplying by i will make 49 positive since i^2=-1.
Of course (2x)^2 = 4x^2.
Hope that explains it.

[StanTheMan]

Oh, I understand now. I forgot that the i stands for root(-1)

[mark79]

Glad I could be of assistance.