To find the roots/zeros, set equal to and solve.

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 out the greatest common factor from each group.

Group the first two terms and the last two terms.

Factor out the greatest common factor (GCF) from each group.

Factor the polynomial by factoring out the greatest common factor, .

Rewrite as .

Factor.

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, where and .

Remove unnecessary parentheses.

Remove unnecessary parentheses.

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 .

Subtract from both sides of the equation.

Set the next factor equal to .

Subtract from both sides of the equation.

Set the next factor equal to .

Add to 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 )

(Multiplicity of )

(Multiplicity of )

Identify the Zeros and Their Multiplicities f(x)=x^4+5x^3-9x^2-45x