If x^2 - x - 1 = 0, what is the value of x^3 - 2x^2?
Divide the polynomial $x^3 -2x^2$ by the polynomial $x^2-x-1$. The remainder is the answer. Do you see why this is correct?
Rewrite x2−x−1=0 as
x2=x+1 (1)
Mutiply (1) by x
x3=x2+x Rewrite as
x3−x2=x (2)
Subtract (1) from (2)
x3−x2−x2=x−(x+1)
Simplify
x3−2x2=−1
