Question

Write the linear factorization of f(x)=x^4 - 2x^3 + 2x - 1

Answer 1

`f(x)=x^4-2x^3+2x-1=x^4-x^3-x^3+x+x-1\\\\=x^3(x-1)-x(x^2-1)+1(x-1)\\\\=x^3(x-1)-x(x^2-1^2)+1(x-1)\\\\=x^3(x-1)-x(x+1)(x-1)+1(x-1)\\\\=x^3(x-1)+(x-1)(-x(x+1)+1)\\\\=(x-1)(x^3-x(x+1)+1)\\\\=(x-1)(x^3-x^2-x+1)\\\\=(x-1)[x^2(x-1)-1(x-1)]\\\\=(x-1)(x-1)(x^2-1)\\\\=(x-1)(x-1)(x^2-1^2)\\\\=(x-1)(x-1)(x-1)(x+1)`

`Used:\\\\a^2-b^2=(a-b)(a+b)`