Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

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 .

Raise to the power of .

Multiply by .

Subtract from .

Multiply by .

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.

Factor using the perfect square rule.

Rewrite as .

Check the middle term by multiplying and compare this result with the middle term in the original expression.

Simplify.

Factor using the perfect square trinomial rule , where and .

Combine like factors.

Raise to the power of .

Use the power rule to combine exponents.

Add and .

If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .

Set the first factor equal to .

Take the square root of both sides of the equation to eliminate the exponent on the left side.

The complete solution is the result of both the positive and negative portions of the solution.

Simplify the right side of the equation.

Rewrite as .

Pull terms out from under the radical, assuming positive real numbers.

is equal to .

Set the next factor equal to .

Set the equal to .

Add to both sides of the equation.

The final solution is all the values that make true.

Find the Roots (Zeros) x^5-3x^4+3x^3-x^2=0