How to determine if a factor is a factor of a polynomial using factor theorem

The video tutorial explains how to determine if x-3 is a factor of a polynomial using the factor theorem. It begins with a basic understanding of factors, then applies this to polynomials. The factor theorem is introduced as a method to check if x-3 is a factor by plugging in values and checking for a remainder of zero. The tutorial concludes by verifying the factorization without using long or synthetic division.

What is the primary question being addressed in the first section?

• How to solve quadratic equations?

• Is x minus 3 a factor of a polynomial?

• How to perform long division?

• What is the remainder theorem?

According to the factor theorem, what should be the result when a zero is plugged into the function?

• The result should be 1

• The result should be negative

• The result should be undefined

• The result should be 0

What is the relationship between x minus 3 and x equals 3 in the context of the factor theorem?

• Both are zeros

• x minus 3 is the factor, x equals 3 is the zero

• x minus 3 is the zero, x equals 3 is the factor

• Both are factors

In the practical example, what is the result of the polynomial calculation when x equals 3?

• The result is 18

• The result is -18

• The result is 0

• The result is 27

Why is it unnecessary to perform long division in the final section?

• Because the polynomial is too complex

• Because the factor theorem already proved x minus 3 is a factor

• Because long division is not applicable

• Because synthetic division is preferred