Factor completely x^4-17x^2+16

(x - 1) (x + 1) (x - 4) (x + 4)

Step-by-step explanation:

actor the following:

x^4 - 17 x^2 + 16

x^4 - 17 x^2 + 16 = (x^2) ^2 - 17 x^2 + 16:

(x^2) ^2 - 17 x^2 + 16

The factors of 16 that sum to - 17 are - 1 and - 16. So, (x^2) ^2 - 17 x^2 + 16 = (x^2 - 1) (x^2 - 16):

(x^2 - 1) (x^2 - 16)

x^2 - 16 = x^2 - 4^2:

(x^2 - 1) (x^2 - 4^2)

Factor the difference of two squares. x^2 - 4^2 = (x - 4) (x + 4):

(x - 4) (x + 4) (x^2 - 1)

x^2 - 1 = x^2 - 1^2:

(x^2 - 1^2) (x - 4) (x + 4)

Factor the difference of two squares. x^2 - 1^2 = (x - 1) (x + 1):

Answer: (x - 1) (x + 1) (x - 4) (x + 4)