How do you find all rational roots for #x^5 - 2x^4 + 11x^3 - 22x^2 - 12x + 24 = 0#?
We will use the Rational Root Theorem:
If the rational number r/s is a root of a polynomial whose coefficients are integers, then the integer r is a factor of the constant term, and the integer s is a factor of the leading coefficient.
r=24 and s=1
So the rational roots must be factor of 24/1=24:
By trying these possible roots, we discover that
If we divide the polynom by