# Factor over the Complex Numbers 11x^4-x^3-33x^2+575x-52

Factor using the rational roots test.
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 and simplify the expression. In this case, the expression is equal to so is a root of the polynomial.
Substitute into the polynomial.
Raise to the power of .
Multiply by .
Raise to the power of .
Multiply by .
Subtract from .
Raise to the power of .
Multiply by .
Subtract from .
Multiply by .
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.
Multiply by .
Factor using the rational roots test.
Factor using the rational roots test.
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 and simplify the expression. In this case, the expression is equal to so is a root of the polynomial.
Substitute into the polynomial.
Raise to the power of .
Multiply by .