How to Find Remaining Factors When Given One Factor, Synthetic Division

The video tutorial explains how to factor a polynomial completely. It begins with an introduction to the polynomial and a given factor, followed by an explanation of factors using the number 12 as an example. The tutorial then discusses methods for dividing polynomials, specifically long division and synthetic division. It guides viewers through finding all factors of a polynomial and emphasizes the importance of factoring polynomials into linear factors. The tutorial concludes by finalizing the factorization process, ensuring all factors are identified and expressed as linear factors.

What is the definition of a factor in the context of numbers?

• A number that can be subtracted from another to get zero

• A number that is always greater than the original number

• A number that divides another number without leaving a remainder

• A number that can be added to another to get a sum

What is the main advantage of using synthetic division over long division for polynomials?

• It can be used for any polynomial, regardless of the factor

• It is faster and simpler when the factor is linear

• It provides an exact solution for all types of equations

• It requires fewer steps and less calculation

What is the result of dividing the polynomial X^3 - 6X^2 + 11X - 6 by X - 3 using synthetic division?

• X^2 - 2X + 3

• X^2 - 3X + 2

• X^2 + 3X - 2

• X^2 + 2X - 3

What is the next step after obtaining a quadratic factor from synthetic division?

• Leave it as it is

• Add it to the original polynomial

• Multiply it by the original polynomial

• Factor it further into linear factors

What are the complete linear factors of the polynomial X^3 - 6X^2 + 11X - 6?

• (X + 1), (X - 2), (X + 3)

• (X - 1), (X + 2), (X - 3)

• (X + 1), (X + 2), (X + 3)

• (X - 1), (X - 2), (X - 3)