How would you factor 4x^2 + 9?
I think the answer has imaginary numbers in it, but how would you get the solution?

Question

How would you factor 4x^2 + 9?
I think the answer has imaginary numbers in it, but how would you get the solution?

anonymous · Answer

4x^2 = -9
x^2 = -9/4
x = +/- SQRT(-9/4)
x = +/- 3/2(i)

anonymous · Answer

Couldn't you just do the square root of both sides to get 
2x= SQRT(-9)
?

accessdenied · Answer

you would get 2x = +- sqrt(-9)

anonymous · Answer

Oh yeah the +/-, but besides that, that way works?

anonymous · Answer

yes

anonymous · Answer

Okay. Thanks :)

accessdenied · Answer

I suppose theoretically, we could use difference of squares to factor this, asserting that the expression can be rewritten as "4x^2 - 9(i^2)", which would factor into (2x + 3i)(2x - 3i).
In practice, however, we would simply say it is not factorable because we usually look for integers when factoring.

anonymous · Answer

It says to find all real and imaginary factors. So it would be (2x-3i)(2x+3i)

accessdenied · Answer

ah, well, that may work for your situation then.  :P
ive never been asked to find imaginary factors for polynomials in my algebra classes.  D: