When Given a Polynomial & Its Factors Find All Zeros and Write as a Product of its Factors

The video tutorial covers solving polynomial equations with fractions using synthetic division. It explains the process of finding zeros, applying the division algorithm, and factorizing polynomials. The tutorial emphasizes the importance of obtaining a remainder of zero and demonstrates how to write a polynomial as a product of its factors, ultimately finding all zeros.

Why is it important to set factors in the form of X - K equal to zero?

• To determine the zeros of the function

• To simplify the function

• To find the maximum value of the function

• To convert the function into a polynomial

What is a crucial outcome when performing synthetic division?

• The quotient should be a linear function

• The remainder should be zero

• The coefficients should be integers

• The divisor should be a fraction

What is the first step in applying synthetic division?

• Multiply the coefficients by the divisor

• Select a zero to use

• Add the coefficients together

• Divide the coefficients by the divisor

How can you verify the correctness of synthetic division?

• By ensuring the remainder is zero

• By checking if the quotient is a polynomial

• By comparing with the original polynomial

• By confirming the divisor is a factor

What does multiplying the quotient by the divisor yield?

• A new factor

• A constant value

• The original polynomial

• A linear equation

What is the purpose of linear factorization?

• To express a polynomial as a sum of terms

• To find the maximum value of a polynomial

• To write a polynomial as a product of its factors

• To convert a polynomial into a linear equation

How do you find all the zeros of a polynomial?

• By dividing the polynomial by its highest degree term

• By setting the polynomial equal to a constant

• By setting each factor equal to zero

• By multiplying the polynomial by its derivative