# Identify the Zeros and Their Multiplicities f(x)=3x^6+30x^5+75x^4

To find the roots/zeros, set equal to and solve.
Factor the left side of the equation.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
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 .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide 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 and solve.
Set the first factor equal to .
Take the 4th 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 and solve.
Set the next factor equal to .
Set the equal to .
Subtract from both sides of the equation.
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 )
Identify the Zeros and Their Multiplicities f(x)=3x^6+30x^5+75x^4