Exploring Synthetic Division and the Remainder Theorem

This video tutorial covers synthetic division, a method for dividing polynomials. It begins with an introduction to the concept and its applications, followed by detailed examples of synthetic division and confirmation using long division. The video also explores evaluating functions using the remainder theorem and factoring polynomials. Advanced examples demonstrate complex polynomial division, and the quadratic formula is applied to unfactorable trinomials. The tutorial concludes with a final example and summary of key concepts.

What is the first step in synthetic division when dividing a polynomial by x - 3?

• Set x - 3 equal to -3

• Set x - 3 equal to 3

• Set x - 3 equal to 0

• Set x - 3 equal to 1

When using synthetic division, what do you do after writing down the coefficients of the polynomial?

• Multiply the coefficients by the divisor

• Add the coefficients together

• Bring down the first coefficient

• Divide the coefficients by the divisor

How can you evaluate a function using synthetic division?

• By finding the quotient and remainder

• By setting the function equal to zero

• By using the remainder theorem

• By factoring the polynomial

What is the purpose of finding the zeros of a polynomial function?

• To find the factors of the polynomial

• To confirm the polynomial's leading coefficient

• To determine the degree of the polynomial

• To evaluate the function at specific points

Which of the following is a potential factor of the polynomial x^3 - 7x + 6?

• x + 1

• x + 3

• x - 2

• x - 1

What is the result of factoring x^3 by x - 2?

• x^2 + 2

• x^2 - 4

• x^2 + 4

• x^2 - 2

Which of the following is a possible zero of the polynomial 3x^3 - x^2 + 7x + 6?

• 3

• 1

• 6

• 2

What is the first step in synthetic division?

• Divide the first coefficient by the divisor

• Add the coefficients

• Bring down the first coefficient

• Multiply the divisor by the first coefficient

What is the factor form of the polynomial x^4 - x^3 + 2x^2 - 4x - 8?

• (x - 1)(x^3 + 2x^2 - 4x + 8)

• (x + 1)(x^3 - 2x^2 + 4x - 8)

• (x + 1)(x^3 + 2x^2 - 4x + 8)

• (x - 1)(x^3 - 2x^2 + 4x - 8)

What are the real solutions for the polynomial x^4 - x^3 - 11x^2 + 5x + 30?

• 2, 3, √5, -√5

• -2, -3, √5, -√5

• 2, -3, √5, -√5

• -2, 3, √5, -√5