Find All the Zeros using P Over Q Rational Zero Test

The video tutorial explains how to find the zeros of a polynomial using the P/Q method, Carts Rule of Signs, synthetic division, and factoring. It begins by identifying the factors of the constant and leading coefficient, then uses Carts Rule to determine the number of positive and negative real zeros. The tutorial demonstrates synthetic division to verify zeros and concludes with factoring the polynomial to find all zeros.

What does P represent in the P/Q method?

• Factors of the leading coefficient

• Factors of the constant term

• The degree of the polynomial

• The sum of the coefficients

According to Descartes' Rule of Signs, what does a variation in sign indicate?

• The sum of the coefficients

• The number of positive real zeros

• The degree of the polynomial

• The number of terms in the polynomial

How many positive zeros are there according to Descartes' Rule of Signs?

• None

• Three

• Two

• One

What is the purpose of using synthetic division in polynomial analysis?

• To find the degree of the polynomial

• To confirm a zero and find factors

• To determine the leading coefficient

• To calculate the sum of the roots

What is the result of synthetic division when a zero is confirmed?

• A negative remainder

• A positive remainder

• A remainder of zero

• A remainder equal to the leading coefficient

Which of the following is a factor of the quadratic expression obtained from synthetic division?

• 2x - 5

• x - 2

• 2x + 3

• x + 1

What are the zeros of the polynomial after factoring?

• 1, -5/2, -3/2

• -1, 5/2, 3/2

• 2, -5, -3

• 0, 5, 3