Polynomial Division Concepts and Techniques

The video tutorial explains how to perform polynomial long division, specifically dividing a trinomial by a binomial. The instructor guides through aligning terms, multiplying, subtracting, and handling remainders. The process is verified by multiplying the quotient and divisor to ensure the dividend is obtained. The tutorial emphasizes understanding each step and encourages students to follow along actively.

What is the first step in dividing a trinomial by a binomial using long division?

• Add the binomial to the trinomial

• Multiply the entire trinomial by the binomial

• Determine what to multiply the divisor by to match the leading term of the dividend

• Subtract the binomial from the trinomial

When aligning terms in polynomial division, where should the new term be placed?

• Above the divisor

• Above the term with the same degree

• Above the leading term of the dividend

• Above the constant term

What is the purpose of aligning terms in polynomial division?

• To avoid errors in addition

• To simplify the division process

• To ensure correct subtraction

• To make multiplication easier

What operation is performed after multiplying the divisor by the determined term?

• Addition

• Subtraction

• Multiplication

• Division

What should be done after subtracting the multiplied terms in polynomial division?

• Add the remainder to the quotient

• Bring down the next term from the dividend

• Divide the remainder by the divisor

• Multiply the remainder by the divisor

How do you determine the next term to bring down in polynomial division?

• Choose the term with the highest degree

• Bring down the next term in the sequence

• Select the term with the lowest coefficient

• Bring down the constant term

What indicates that the division process is complete?

• The remainder is zero

• The quotient is a constant

• The divisor is fully multiplied

• The dividend is fully subtracted

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

• Divisor minus quotient equals dividend

• Divisor plus quotient equals dividend

• Divisor divided by quotient equals dividend

• Divisor times quotient equals dividend

In the context of polynomial division, what does 'foil it out' refer to?

• Subtracting the divisor from the dividend

• Aligning the terms

• Simplifying the remainder

• Expanding the product of two binomials

What should be done if there is a remainder after the division process?

• Subtract it from the dividend

• Ignore it

• Add it to the quotient

• Multiply it by the divisor