Find the Zeros of a Polynomial by Factoring Substitution

The video tutorial covers determining the end behavior, finding real zeros, and understanding multiplicity of polynomial functions. It explains the role of degree and leading coefficient in end behavior, and demonstrates solving for real zeros using factoring, the quadratic formula, and completing the square. The zero product property is applied to solve equations, and the concept of complex numbers is introduced, highlighting their impact on real roots and multiplicity.

What determines the end behavior of a polynomial function?

• The x-intercepts

• The number of terms

• The degree and leading coefficient

• The constant term

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

• Finding the derivative

• Identifying the leading coefficient

• Setting the function equal to zero

• Graphing the function

Which method is NOT typically used to solve for real zeros?

• Factoring

• Differentiation

• Completing the square

• Using the quadratic formula

What is the zero product property used for?

• To find the degree of a polynomial

• To determine the end behavior

• To solve equations set to zero

• To identify the leading coefficient

What is the purpose of writing a 'key' when factoring?

• To simplify the polynomial

• To find the x-intercepts

• To identify the leading coefficient

• To convert the polynomial into a quadratic form

How is multiplicity identified in a polynomial?

• By the leading coefficient

• By the exponents of the factors

• By the degree of the polynomial

• By the constant term

What happens when you take the square root of a negative number in the context of polynomial roots?

• You find a real root

• You find an imaginary root

• You find a complex root

• You find a rational root