## itsjustme_lol 2 years ago Im having trouble with factoring..

1. itsjustme_lol

im suppose to factor x^2+4 is this prime?

2. itsjustme_lol

or (x+2)(x+2)

3. hartnn

it will have complex factors. else its prime.

4. hartnn

its NOT (x+2)(x+2)

5. hartnn

\[a^2+b^2 = (a+ib)(a-ib)\]

6. itsjustme_lol

ok wait a second

7. itsjustme_lol

(x + 2)(x – 2) (x + 2)(x + 2) (x + 1)(x + 4) ao it couldnt be any of these? im so confused with this one question

8. hartnn

no, it cannot be any of these. its prime, if we are considering only real factors.

9. itsjustme_lol

ok. thankyou. i thought so, just was not sure. :) i appreicaite that.

10. whpalmer4

\[(x+2)(x-2) = x^2 +2x - 2x -4 = x^2 -4\]\[(x+2)(x+2) = x^2 + 2x + 2x + 4 = x^2 + 4x + 4\]\[(x+1)(x+4) = x^2 + x + 4x + 4 = x^5 + 5x + 4\]

11. whpalmer4

That i in there in the (a+ib)(a-ib) does the trick of reversing the sign of the final term: \[(a+ib)(a-ib) = a^2 + aib - aib -i^2b^2 = a^2 - i^2b^2\]but \[ i^2 = -1\] so \[a^2-i^2b^2=a^2-(-b^2)=a^2+b^2\]

12. hartnn

welcome ^_^