Exploring Polynomial Long Division Techniques

The video tutorial covers polynomial long division, explaining its importance when factorization isn't possible. It provides two examples: dividing a trinomial by a binomial and handling a polynomial with a zero coefficient. The instructor emphasizes the division algorithm, detailing each step and the importance of maintaining columns for each term.

Why might factoring and reducing not always be sufficient for polynomial division?

• Because polynomials are always factorable.

• Because reducing is not a valid method.

• Because polynomials may not share common factors.

• Because factoring is always easier.

What is the first step in performing polynomial long division?

• Multiplying the polynomials.

• Factoring the polynomials.

• Adding the polynomials.

• Following the division algorithm.

In the first example, what do you multiply X by to get x squared?

• X

• X squared

• 5

• 1

Where do you place the result of multiplying X by X in the polynomial long division?

• In the constant column

• In the X column

• In the X squared column

• In the remainder column

What do you do after multiplying and placing the terms in polynomial long division?

• Subtract the terms

• Change the signs and add down

• Add the terms

• Multiply again

What is the next step after bringing down the next term in polynomial long division?

• Add the terms

• Multiply by the divisor

• Divide by the divisor

• Change the signs

Why is it important to include zero coefficients in polynomial long division?

• To ensure every term has a column

• To avoid mistakes

• To simplify the polynomial

• To make the division easier

In the second example, what do you multiply X by to get 2x to the third?

• 4

• 2

• X

• 2x squared

What is the result of changing the signs and adding down in polynomial long division?

• The terms cancel out

• The terms are multiplied

• The terms are added

• The terms are divided

How do you handle the remainder in polynomial long division?

• Subtract it from the quotient

• Ignore it

• Write it over the divisor

• Add it to the quotient