X^4+3x^2-28
how to factorize it?

(x^2 - 4) (x^2 + 7) is the answer
x^2 × x ^2 = x ^4
x^2 × 7 = 7x^2
x^2 x -4 = -4x^2
Those two steps combined = 3x^2
-4 × 7 = 28

To factor this we need to use the reverse of the foil method. FOIL first, outside, inside, last.  (A+B)(C+D) what times what (?+B)(?+D)will give you x^4?  (x^2+b)(x^2+D). Next, what will give you -28 (A+?)(C+?) Several numbers will work but we want -4 and 7. This is why.. (x^2-4)(x^2+7) First times first gives you x^4 Outside times outside give you 7x^2 Inside times inside is -4x^2 and last times last is -28. combine 7x^2 and -4x^2 and you get your original middle number of 3x^2. now you know that (x^2-4)(x^2+7) is correct. Hope you learned something..

Absolute value graph shifted point 5 up