Understanding the Factor Theorem

The video tutorial explains the factor theorem, a special case of the remainder theorem, used to find factors of polynomials. It guides viewers through the process of substituting values to find zeros, using prime factorization to identify potential factors, and testing values systematically. The tutorial also demonstrates polynomial long division to confirm factors and reduce polynomials to simpler forms.

What is the first step in using the factor theorem on a polynomial?

• Start with a factorized form

• Use synthetic division immediately

• Substitute values into the polynomial

• Divide the polynomial by a random number

Why is the number 90 significant in the context of the factor theorem?

• It is a common factor of all terms

• It is the degree of the polynomial

• It provides a clue for finding factors

• It is the sum of all coefficients

What is the prime factorization of 90?

• 2, 3, 5

• 2, 3, 3, 5

• 3, 3, 5

• 2, 5, 5

When testing values for factors, which should you try first?

• Only positive numbers

• Random numbers

• Divisors of the constant term

• Values far from zero

If initial guesses for factors do not work, what should you do next?

• Test values that are not divisors

• Stop testing altogether

• Continue testing randomly

• Use the next set of divisors

What is the result when a polynomial is divided by one of its factors?

• A quotient with a remainder

• A remainder of zero

• A remainder equal to the factor

• A larger polynomial

What is the next step after finding a factor of a quartic polynomial?

• Stop the process

• Factorize the quotient

• Multiply the factor back

• Ignore the factor

What is the purpose of reducing a polynomial to a quadratic?

• To increase the degree

• To simplify the factorization process

• To eliminate all factors

• To make it more complex

What is the term for the result of dividing a polynomial by one of its factors?

• Quotient

• Product

• Remainder

• Dividend

Why is it important to rehearse the division process multiple times?

• To find new factors

• To increase the polynomial's degree

• To ensure accuracy and understanding

• To memorize the polynomial