Exploring Polynomial Long Division and Synthetic Methods

This video tutorial covers dividing polynomials using long division, synthetic division, and synthetic substitution. It explains how to determine if a polynomial is a factor and includes examples with step-by-step instructions. The tutorial also addresses handling missing terms and using fractions in synthetic substitution.

What are the main topics covered in the video on dividing polynomials?

• Factoring polynomials, polynomial identities, and polynomial functions

• Long division, synthetic division, synthetic substitution, and determining factors

• Addition, subtraction, multiplication, and division of polynomials

• Graphing polynomials, solving polynomial equations, and polynomial inequalities

What is the first step in setting up a polynomial for long division?

• Arrange the polynomial in ascending order

• Simplify the polynomial

• Arrange the polynomial in descending order

• Factor the polynomial

When performing long division, what should you do if there are gaps in the exponents?

• Skip the division process

• Fill in the gaps with zeros

• Ignore the gaps

• Replace the gaps with ones

In long division, what do you do after subtracting the terms?

• Divide the terms

• Multiply the terms

• Add the terms

• Bring down the next term

What is the remainder in polynomial long division?

• The dividend

• The leftover term after division

• The divisor

• The quotient

What is the first step in synthetic division?

• Multiply the coefficients

• Subtract the coefficients

• Fill in the coefficients, including zeros for missing exponents

• Divide the coefficients

In synthetic division, what do you do with the divisor?

• Use the same sign as given

• Use the opposite sign

• Multiply the divisor by 2

• Ignore the divisor

What does synthetic substitution help determine?

• The roots of the polynomial

• The value of the polynomial at a given point

• The degree of the polynomial

• The factors of the polynomial

How do you determine if a polynomial is a factor of another polynomial?

• If the dividend is zero

• If the quotient is zero

• If the divisor is zero

• If the remainder is zero

What should you do if the remainder is not zero when determining factors?

• The polynomial is a factor

• The polynomial is not a factor

• The polynomial is the quotient

• The polynomial is the divisor