Find the Zeros of a Polynomial Given One Zero as a Fraction

The video tutorial explains how to find zeros of a polynomial using the rational zero test and synthetic division. It covers the process of identifying factors, performing synthetic division, and solving quadratic equations to find all possible zeros, including rational, irrational, and complex numbers.

What does it mean if a factor evenly divides a polynomial?

• The factor is a zero of the polynomial.

• The factor is a constant term.

• The factor is a leading coefficient.

• The factor is an imaginary number.

Which of the following is a step in the Rational Zero Test?

• Determining the polynomial's imaginary zeros.

• Identifying factors of the constant term.

• Finding the derivative of the polynomial.

• Calculating the polynomial's degree.

Which of the following is a possible rational zero of a polynomial with a constant term of 15 and a leading coefficient of 4?

• ± 3/2

• ± 2/1

• ± 5/3

• ± 7/4

What is the purpose of synthetic division in polynomial analysis?

• To find the derivative of a polynomial.

• To determine the degree of a polynomial.

• To divide polynomials and find factors.

• To calculate the imaginary zeros of a polynomial.

When solving a quadratic equation, what is the first step if the equation is factorable?

• Find the imaginary zeros.

• Calculate the derivative.

• Factor out the greatest common factor.

• Use the quadratic formula.

How many zeros should a polynomial of degree three have?

• Three

• Four

• One

• Two

What is the result of applying the zero product property to a factored polynomial equation?

• The polynomial's factors are multiplied.

• The polynomial's zeros are identified.

• The polynomial's degree is reduced.

• The polynomial's imaginary zeros are calculated.