# Simple factoring question

1. Jan 23, 2009

### hockeyfghts5

1. The problem statement, all variables and given/known data

can u factor x2+4
and cant seem to remember the the difference of cubes and isn't there another special cubed theorem.

2. Relevant equations

3. The attempt at a solution

2. Jan 23, 2009

### rock.freak667

It can be factored but it won't be factored with real numbers. You'd need to introduce the imaginary constant,i, such that i2=-1 and use that to factor.

3. Jan 23, 2009

### Staff: Mentor

x2 + 4 = (x + 2i)(x - 2i), where i is the imaginary unit rock.freak667 mentioned.
Here are the sum and difference of cubes formulas:
x3 + a3 = (x + a)(x2 - ax + a2)
x3 - a3 = (x - a)(x2 + ax + a2)

4. Jan 23, 2009

### hockeyfghts5

thanks, so i have another question if someone can help me.

lim x3-62+11x-6
x->-1 x3-4x2-19x +14
i cant seem how to factor the top out if i even need to do that or the bottom

5. Jan 23, 2009

### rock.freak667

Why would you need to factor it? Did you evaluate it at x=-1? Was it in the indeterminate form 0/0?

6. Jan 23, 2009

### Fermat

If the numerator, or denominator, goes to zero when x = 1, then (x-1) is a factor.

You can factor it out by dividing (x-1) into the numerator, say, in the style of long-division.