If a polynomial function has integer coefficients, then every rational zero will have the form where is a factor of the constant and is a factor of the leading coefficient.
Find every combination of . These are the possible roots of the polynomial function.
Substitute into the polynomial.
Simplify each term.
Raise to the power of .
Raise to the power of .
Multiply by .
Multiply by .
Subtract from .
Add and .
Subtract from .
Since is a known root, divide the polynomial by to find the quotient polynomial. This polynomial can then be used to find the remaining roots.
Divide by .
Write as a set of factors.
Write as a Set of Linear Factors x^3-9x^2+22x-12