How to divide two polynomials using long division

The video tutorial covers division problems, focusing on factors and polynomial division. It begins with an introduction to division and factor trees, then explains polynomial factors and the zero product property. The tutorial proceeds to set up and perform polynomial long division, emphasizing the importance of standard form and handling remainders. The process is detailed step-by-step, ensuring clarity in understanding polynomial division.

What is a common characteristic of factors in a factor tree?

• They multiply to form a larger number.

• They are always even numbers.

• They are always prime numbers.

• They divide into the number evenly.

What does it mean if a polynomial has a remainder of zero when divided by another polynomial?

• The division is incorrect.

• The dividend is a factor.

• The divisor is a factor.

• The divisor is not a factor.

What is the zero product property used for in polynomial factorization?

• To find the zeros or solutions of a polynomial.

• To find the factors of a polynomial.

• To divide polynomials.

• To multiply polynomials.

Why is it important to have polynomials in standard form before division?

• To avoid using placeholders.

• To simplify the polynomial.

• To make the division faster.

• To ensure all terms are accounted for.

What is the purpose of using a placeholder like 0X in polynomial division?

• To change the polynomial.

• To simplify the division.

• To maintain place value for missing terms.

• To avoid subtraction errors.

What happens when you subtract a negative term in polynomial division?

• It doubles the term.

• It becomes zero.

• It remains negative.

• It becomes a positive term.

Why can't you subtract terms with different powers in polynomial division?

• They are not like terms.

• It changes the polynomial.

• It simplifies the division.

• It is unnecessary.

How do you write the final answer if there is a remainder in polynomial division?

• Just write the quotient.

• Write the quotient and add the remainder over the divisor.

• Ignore the remainder.

• Subtract the remainder from the quotient.

What is the result when a larger power divides into a smaller power in polynomial division?

• The dividend is a factor.

• The divisor is a factor.

• The division is complete.

• A remainder is formed.

What should you do if there is no remainder in polynomial division?

• Write the quotient only.

• Add a placeholder.

• Multiply the quotient.

• Subtract the divisor.