# Identify the Zeros and Their Multiplicities -1/3x(x^2-25)^2

To find the roots/zeros, set equal to and solve.
Multiply both sides of the equation by .
Simplify both sides of the equation.
Simplify .
Cancel the common factor of .
Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply.
Multiply by .
Multiply by .
Multiply by .
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 .
Set the next factor equal to and solve.
Set the next factor equal to .
Factor the left side of the equation.
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Apply the product rule to .
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 and solve.
Set the first factor equal to .
Set the equal to .
Subtract from both sides of the equation.
Set the next factor equal to and solve.
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.
The final solution is all the values that make true. The multiplicity of a root is the number of times the root appears.
(Multiplicity of )
(Multiplicity of )
(Multiplicity of )
Identify the Zeros and Their Multiplicities -1/3x(x^2-25)^2
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