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Question:
Solve the equation
x^3-13x^2+47x-35=0 given that 1 is zero of f(x)=x^3-13x^2+47x-35
Solution:
Knowing that 1 is a zero (as evident by the factor theorem), we divide the expression by (x-1) to get
(x^3-13x^2+47x-35)/(x-1)=x^2-12x+35
the latter factorizes into (x-7)(x-5)
from which we can conclude that the solutions to x^3-13x^2+47x-35=0 are
x={1,5,7}
