Find the zeros and multiplicity by factoring a polynomial

The video tutorial covers the process of factoring polynomials, starting with identifying common factors and moving on to quadratic equations. It explains the concept of multiplicity in zeros, using the zero product property to find zeros, and discusses how coefficients affect the zeros of a polynomial. The tutorial emphasizes understanding these concepts for solving equations and preparing for quizzes or tests.

What is the first step in solving for zeros in a polynomial equation?

• Multiply all terms by zero

• Set the equation to zero and factor out common factors

• Add all coefficients together

• Divide the equation by the highest power of x

How can X to the 4th power be factored?

• X - 4 * X - 1

• X + 4 * X + 1

• X^2 + 4

• X * X * X * X

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

• The repetition of the same zero multiple times

• The degree of the polynomial

• The number of different variables in the equation

• The sum of all coefficients

What happens to the coefficient when using the zero product property?

• It is added to the zeros

• It is multiplied by the zeros

• It is divided out and does not affect the zeros

• It changes the zeros of the polynomial

Why should the coefficient not affect your calculation of zeros?

• Because it is always zero

• Because it is irrelevant to the polynomial

• Because it divides out and does not change the zeros

• Because it is a constant