Solving a Polynomial by Factoring to Find Zeros & Determine Multiplicity

The video tutorial explains how to find the zeros of a polynomial equation by setting it equal to zero, factoring it, and applying the zero product property. It also covers the concept of multiplicity, how to factor equations into linear forms, and how multiplicity affects the graph's behavior.

What is the first step in finding the zeros of a polynomial equation?

• Set the equation equal to zero

• Multiply all terms by a constant

• Find the derivative

• Graph the equation

When applying the zero product property, what must you remember when taking square roots?

• Only consider positive roots

• Ignore the roots

• Only consider negative roots

• Consider both positive and negative roots

What does the term 'multiplicity' refer to in the context of polynomial zeros?

• The sum of all zeros

• The product of all zeros

• The degree of the polynomial

• The number of times a zero appears

How can you determine the multiplicity of a zero?

• By adding all coefficients

• By graphing the polynomial

• By factoring the polynomial into linear factors

• By finding the derivative

What happens to the graph of a polynomial at a zero with even multiplicity?

• The graph touches the x-axis and turns around

• The graph becomes undefined

• The graph crosses the x-axis

• The graph remains constant