Finding Zeros of Polynomials

The video tutorial covers methods to find zeros of a polynomial, including factoring, the rational zero test, and Cart's rule of signs. It explains how to apply synthetic division and the quadratic formula to identify real and complex zeros. The tutorial emphasizes understanding the process without relying on graphing technology.

What is the first step in finding the zeros of a polynomial when no zeros are given?

• Graph the polynomial

• Apply the Rational Zero Test

• Factor the polynomial

• Use the quadratic formula

Which of the following is a possible rational zero of a polynomial with a leading coefficient of 1 and a constant term of 10?

• 9

• 5

• 7

• 3

What is the Rational Zero Test used for?

• To solve quadratic equations

• To identify possible rational zeros

• To find the factors of a polynomial

• To determine the degree of a polynomial

According to the Rule of Signs, how many positive real zeros can a polynomial have if there are three sign changes?

• Three or one

• Two or zero

• Four or two

• One or zero

How do you determine the number of negative real zeros using the Rule of Signs?

• Count the number of positive terms

• Count the sign changes in f(x)

• Count the number of negative terms

• Count the sign changes in f(-x)

What is the purpose of using synthetic division in finding polynomial zeros?

• To test if a number is a zero of the polynomial

• To simplify the polynomial

• To find the derivative of the polynomial

• To find the maximum value of the polynomial

What is the result of synthetic division if a number is a zero of the polynomial?

• A negative remainder

• A positive remainder

• A remainder equal to the leading coefficient

• A remainder of zero

If a polynomial has one positive real zero, what type are the other two zeros likely to be?

• Rational

• Whole numbers

• Complex

• Negative

Which method can be used to find complex zeros of a polynomial?

• Graphing

• Synthetic division

• Quadratic formula

• Long division

What is the next step after finding a quotient polynomial using synthetic division?

• Use the quadratic formula to find remaining zeros

• Apply the Rule of Signs

• Graph the quotient polynomial

• Perform long division