Show all work to factor x4 − 17x2 + 16 completely.

ANSWER:  

factors of given expressions are (x -4), (x + 4), (x -1), (x + 1).

SOLUTION:

Given, expression is -- eqn 1

It is an bi–quadratic expression, which means it will have 4 factors.

Now, let us take and put it in eqn (1)

This is an quadratic expression, we can solve this expression by factorizing method.

t(t – 16) – 1(t – 16)  

(t – 16)(t – 1)  

Now, again replace t with  

By using the formula we get

(x – 4)(x + 4)(x -1)(x +1)

Hence, the factors of given expressions are (x -4), (x + 4), (x -1), (x + 1).