Factor the polynomial completely

Question

Factor the polynomial completely

 

x^4 - 40^2 + 39

 

 

 

Answer 1

Assuming this is supposed to be x⁴ - 40x² + 39, this factors as

 

(x² - 1)(x² - 39) =(x + 1)(x - 1)(x + √39)(x - √39)

Answer 2

Factor x⁴ - 40x² + 39

 

Using a substitution of y=x², the problem becomes:  factor y²-40y+39

 

This factors as (y-1)(y-39)

 

Now, remember that y=x²:

  (x² - 1)(x² - 39) 

 and remember that (x² - a²) = (x+a)(x-a)             [actually, a pattern is more substitution]

 

  (x + 1)(x - 1)(x + √39)(x - √39)