Identify the Zeros and Their Multiplicities x^3-15x^2+75x-125

Math
To find the roots/zeros, set equal to and solve.
Factor the left side of the equation.
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Factor using the rational roots test.
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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.
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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.
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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.
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Raise to the power of .
Use the power rule to combine exponents.
Add and .
Set the equal to .
Add to both sides of the equation.
(Multiplicity of )
Identify the Zeros and Their Multiplicities x^3-15x^2+75x-125


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