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.

Factor using the AC method.

Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .

Write the factored form using these integers.

Remove unnecessary parentheses.

Divide each term in by .

Simplify .

Simplify terms.

Cancel the common factor of .

Cancel the common factor.

Divide by .

Apply the distributive property.

Simplify the expression.

Multiply by .

Move to the left of .

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

Multiply by by adding the exponents.

Multiply by .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Multiply by .

Multiply by by adding the exponents.

Move .

Multiply by .

Multiply by .

Subtract from .

Divide by .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor.

Factor using the AC method.

Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .

Write the factored form using these integers.

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 .

Add to both sides of the equation.

Set the next factor 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 )

(Multiplicity of )

Identify the Zeros and Their Multiplicities f(x)=4x^3-12x^2-16x