Apply synthetic division to division of two polynomials

The video tutorial covers division, focusing on factors and synthetic division. It explains how to determine if a number or expression is a factor, the process of synthetic division, and how to find zeros of polynomials. The tutorial provides a step-by-step guide on performing synthetic division, understanding quotients, and finding solutions. It emphasizes the importance of setting factors to zero and using linear divisors in synthetic division.

What is a factor in the context of division?

• A number that is always less than the divisor

• A number that divides another number without leaving a remainder

• A number that multiplies with another to give a product

• A number that is always greater than the dividend

How can you find the zeros of a polynomial?

• By adding the factors

• By dividing the factors

• By multiplying the factors

• By setting the factors equal to zero

What is the key condition for using synthetic division?

• The divisor must be a constant

• The divisor must be linear

• The divisor must be cubic

• The divisor must be quadratic

In synthetic division, what should you do if a term is missing?

• Ignore the missing term

• Add a zero in place of the missing term

• Repeat the previous term

• Add a one in place of the missing term

What does the quotient represent in synthetic division?

• A factor of the original polynomial

• The remainder of the division

• The divisor of the polynomial

• The sum of the polynomial terms

What is the process of rewriting a polynomial as a product of factors called?

• Addition

• Division

• Multiplication

• Factoring

How many zeros can a polynomial have?

• None

• As many as its degree

• Only one

• Exactly two

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

• A remainder equal to the dividend

• A remainder of one

• A remainder of zero

• A remainder equal to the divisor

What should you do with the quotient obtained from synthetic division?

• Ignore it

• Add it to the original polynomial

• Multiply it by the divisor

• Use it as a factor to find more zeros

What is the relationship between the divisor and the quotient in polynomial division?

• The divisor is always less than the quotient

• The divisor and quotient add up to the original polynomial

• The divisor and quotient multiply to give the original polynomial

• The divisor is always greater than the quotient