How to use long division to understand linear factorization and zeros

The video tutorial explains the embedded nature of math and guides students through finding zeros and testing factors of polynomials. It covers the process of polynomial long division, emphasizing the use of placeholders to maintain alignment. The tutorial also discusses the factor theorem, focusing on quadratic factors and how to express polynomials in terms of their factors. The session concludes with a demonstration of finding zeros using the quadratic formula and completing the square.

What is the first step in checking if a term is a factor of a polynomial?

• Subtract the term from the polynomial

• Divide the polynomial by the term

• Multiply the term by the polynomial

• Add the term to the polynomial

Why is it important to align terms correctly during polynomial division?

• To make the division process faster

• To simplify the polynomial

• To ensure the terms are multiplied correctly

• To avoid combining unlike terms

What role do placeholders play in polynomial division?

• They make multiplication easier

• They eliminate the need for subtraction

• They help in aligning terms correctly

• They simplify the polynomial

What is the significance of the factor theorem in polynomial division?

• It helps in multiplying polynomials

• It identifies if a term is a factor of a polynomial

• It simplifies the polynomial

• It determines the degree of the polynomial

How can you find the zeros of a polynomial after identifying its factors?

• By setting the factors equal to zero

• By multiplying the factors

• By dividing the factors

• By adding the factors

What method can be used if a polynomial is not factorable?

• Quadratic formula or completing the square

• Synthetic division

• Long division

• Graphical method

What are the zeros of the polynomial discussed in the video?

• ± I, sqrt, 5, two and -, 3

• ± I, sqrt, 5, three and -, 2

• ± I, sqrt, 5, five and -, 0

• ± I, sqrt, 5, four and -, 1