Use synthetic division to divide P(x)=x4−5x2+4P(x) = x^4 - 5x^2 + 4P(x)=x4−5x2+4 by (x−1)(x - 1)(x−1).
x3+x2−4x−4x^3 + x^2 - 4x - 4x3+x2−4x−4, remainder 0
x3−x2−4x+4x^3 - x^2 - 4x + 4x3−x2−4x+4, remainder 0
x3−5x+4x^3 - 5x + 4x3−5x+4, remainder 0
x3+x2+4x+4x^3 + x^2 + 4x + 4x3+x2+4x+4, remainder 0