Factoring x^4—16

Question

The book says the answer is (x²+4) ( x-2)(x+4) 

 

At first I thought it was simply (x²-4) then just simplfy furrther to  ( x-2)(x+4). 

 

Why is " (x²+4) " positive and not negative?

Answer 1

Hi Alex, the answer to this problem is working with the difference of two squares. The difference of two squares, a² - b² is: (a + b) * (a - b).

 

x⁴ - 16 can be written as (x²)² - 4², which is the difference of two squares.  . Using the rule above, this can be factored into (x² - 4) * (x² + 4).

 

Using the rule again, x² - 4 can be factored into: (x - 2) * (x + 2)

 

The factors are: (x - 2), (x + 2), and (x² + 4).

 

To check, simply multiply the three binomials together.

 

Questions?