This is a 4 degree polynomial
linear factorization means find a form (x-b);
where b is a number.
This form (x-b) have to divide exactly
x^4 -4x^3+ 16x -16
theres only one number which 4th power is 16
is 2 ,because 2^4= 2x2x2x2 = 16
this gives a good indication of the way to solve it.
arrange the terms of polynomial
(x^4 - 4x^3) + (16x-16)
x^3(x-4) + 16( x-1)
16(x-1)= 16 (x-4) +48
then reagrupate and add similar terms
x^3(x-4) + 16 (x-4) + 48
(x-4)• ( x^3 + 16) + 48
then f(x) = (x-4)• ( x^3 + 16) + 48
and this means also b= -4
Because the form we are looking for is (x-4)