Algebra Examples

Identify the Zeros and Their Multiplicities
To find the roots/zeros of the function, set the function equal to and solve.
Factor the left side of the equation.
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Regroup terms.
Rewrite as .
Since both terms are perfect cubes, factor using the sum of cubes formula, where and .
Simplify.
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Multiply by .
Raise to the power of .
Factor out of .
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Factor out of .
Factor out of .
Factor out of .
Factor out of .
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Factor out of .
Factor out of .
Add and .
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 .
Set equal to and solve for .
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Set the factor equal to .
Subtract from both sides of the equation.
Solve the equations for . The multiplicity of a root is the number of times the root appears. For example, a factor of would have a root at with multiplicity of .
(Multiplicity of )
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