Answer: 1. x^2-5x+4
2. x^2-7x+6
3. x^3-7x^2+11x-5
4. x-5
Explanation:
1. x^2-6x+5+x-1=
x^2-6x+x+5-1=x^2-5x+4
2. x^2-6x+5-(x-1)=
x^2-6x+5-x+1=
x^2-6x-x+5+1=x^2-7x+6
3. (x^2-6x+5) * (x-1)=
x(x^2-6x+5)-1(x^2-6x+5)=
x^3-6x^2+5x-x^2+6x-5=
x^3-6x^2-x^2+5x+6x-5=x^3-7x^2+11x-5
4. (x^2-6x+5)/(x-1)=
(x^2-x-5x+5)/(x-1)=
(x(x-1)-5(x-1))/(x-1)=
(x-5)(x-1)/(x-1)=x-5