If (x−1) is a factor of ax3−bx2+cx, what is the value of a3−b3+c3?
-3abc
p(x)=ax3−bx2+cx
If (x - 1) is a factor then x = 1 is the zero of polynomial
p(1) = 0
p(1)=a−b+c=0
It can be written as a+(−b)+c=0
We know that if a+b+c=0, then a3+b3+c3=3abc
So, a3+(−b)3+c3=3a(−b)c=−3abc