Understanding the Factor Theorem

The video tutorial explains the factor theorem and its application in determining if x-3 is a factor of a polynomial. It covers the use of long and synthetic division to verify factors and zeros, emphasizing the remainder theorem for validation. The tutorial concludes with a practical example, demonstrating the process of checking if x-3 is a factor by plugging in values and confirming the result.

What is the main question being addressed in the video?

• How to integrate a polynomial function?

• Is x - 3 a factor of a given polynomial?

• What is the derivative of a polynomial?

• How to solve quadratic equations?

Why is 3 considered a factor of 6?

• Because 3 is less than 6

• Because 3 is a prime number

• Because 3 is greater than 6

• Because 3 divides 6 evenly

What are the two methods mentioned for determining if x - 3 is a factor?

• Factoring and expanding

• Integration and differentiation

• Long division and synthetic division

• Graphing and substitution

What is the purpose of using synthetic division in this context?

• To determine if a polynomial can be divided evenly by x - 3

• To check if a polynomial is factorable

• To find the derivative of the polynomial

• To integrate the polynomial

What does the Factor Theorem help determine?

• If a polynomial has a certain factor

• The maximum value of a function

• The integral of a function

• The derivative of a function

How can you use the Factor Theorem to find if x - 3 is a factor?

• By integrating the polynomial from 0 to 3

• By plugging x = 3 into the polynomial and checking if the result is zero

• By finding the derivative at x = 3

• By graphing the polynomial and checking the intercepts

What is the result when you plug x = 3 into the polynomial in the example?

• The result is 5

• The result is 10

• The result is 0

• The result is 15

What does a remainder of zero indicate when using the Factor Theorem?

• The polynomial is undefined

• x - 3 is not a factor of the polynomial

• The polynomial has no factors

• x - 3 is a factor of the polynomial

What is the relationship between x - 3 and x = 3 in the context of the Factor Theorem?

• Both are factors

• x - 3 is the zero, x = 3 is the factor

• Both are zeros

• x - 3 is the factor, x = 3 is the zero

What does the term 'zero' refer to in polynomial functions?

• A point where the polynomial has a maximum value

• A point where the polynomial is undefined

• A point where the polynomial equals zero

• A point where the polynomial has a minimum value