Dividing Polynomials: Long Division Techniques

The video tutorial provides an overview of dividing polynomials, focusing on long division and synthetic division methods. It emphasizes the importance of placeholders in polynomial division and explains how to find factors and zeros. The tutorial also covers evaluating zeros and their significance in graphing polynomials.

Why is it important to include a placeholder for missing degrees in polynomial long division?

• To make the polynomial look longer

• To ensure every degree is accounted for

• To make the division process faster

• To confuse the solver

What is the first step in the long division method for polynomials?

• Dividing the highest degree term of the dividend by the highest degree term of the divisor

• Adding the divisor to the dividend

• Multiplying the divisor by the highest degree term of the dividend

• Subtracting the divisor from the dividend

What does it mean if the remainder is zero in polynomial long division?

• The dividend is zero

• The divisor is zero

• The divisor divides the dividend evenly

• The divisor does not divide the dividend

What are the zeros of the polynomial x^2 - 4x - 12?

• 4 and -3

• 2 and -6

• 3 and -4

• 6 and -2

How can you find the zeros of a polynomial from its factors?

• By multiplying the factors together

• By dividing the factors

• By setting each factor equal to zero

• By adding the factors

In synthetic division, what is 'k'?

• The divisor

• The dividend

• The factor

• The zero

What is the purpose of synthetic division?

• To subtract polynomials

• To add polynomials

• To multiply polynomials

• To find the remainder of a polynomial division

What should you do if you don't know the zero for synthetic division?

• Guess the zero

• Use the highest degree term as the zero

• Set the factor equal to zero and solve

• Ignore the zero

What does it mean if evaluating a function at a zero gives zero?

• The zero is incorrect

• The zero is a factor of the function

• The function is undefined

• The function is constant

What are the intercepts of the graph if the zeros are -4, 6, and -2?

• (4, -6), (-6, 2), (2, -4)

• (-4, 6), (6, -2), (-2, 4)

• (4, 0), (-6, 0), (2, 0)

• (-4, 0), (6, 0), (-2, 0)