Learn How to Find All Zeros of a Polynomial Using Rational Zero Test and Synthetic

The video tutorial explains how to find rational zeros of a polynomial using the P/Q method. It covers testing possible zeros with the remainder theorem and synthetic division. The tutorial also demonstrates factoring and using the zero product property to find zeros. Graphing is used to confirm zeros, and the final solutions are presented.

What is the first step in finding all possible rational zeros of a polynomial?

• Use the quadratic formula

• Graph the polynomial

• Apply the P/Q method

• Perform synthetic division

Which theorem can be used to verify if a number is a zero of a polynomial?

• Binomial Theorem

• Factor Theorem

• Remainder Theorem

• Pythagorean Theorem

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 test potential zeros and factor the polynomial

• To calculate the integral of a polynomial

What is the factor of a polynomial if -1 is a zero?

• X + 2

• X - 2

• X + 1

• X - 1

How can graphing technology assist in finding zeros of a polynomial?

• By providing the exact value of zeros

• By simplifying the polynomial

• By calculating the derivative

• By showing where the graph crosses the x-axis

What is the result when you solve X^2 - 5 = 0?

• X = ±2.5

• X = ±5

• X = ±sqrt(5)

• X = ±10

Which of the following is NOT a zero of the polynomial discussed?

• 3

• -1

• sqrt(5)

• 2