Dividing Polynomials with Long Division Techniques

The video tutorial explains the long division method for dividing polynomials. It emphasizes the importance of understanding this method before learning synthetic division. The instructor sets up a polynomial division problem and guides through the step-by-step process, highlighting common mistakes, especially in subtraction. The tutorial concludes with handling remainders and writing the final answer.

Why is it important to understand the long division method for polynomials?

• It helps in understanding synthetic division better.

• It is the only method to divide polynomials.

• It is faster than other methods.

• It is the default method for all polynomial divisions.

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

• Identifying the remainder.

• Setting up the division like a long division problem.

• Multiplying the polynomials.

• Subtracting the polynomials.

When dividing the leading terms, what do you divide first?

• The middle term.

• The constant term.

• The highest degree term of the dividend by the highest degree term of the divisor.

• The lowest degree term.

What is the result of dividing x^3 by x?

• x^2

• x

• x^3

• 1

What should you do after multiplying the divisor by the quotient term?

• Add the result to the dividend.

• Subtract the result from the dividend.

• Divide the result by the next term.

• Multiply the result by the next term.

Why is it important to remember the negative sign when subtracting?

• It changes the degree of the polynomial.

• It ensures the correct sign of the result.

• It simplifies the division process.

• It helps in identifying the remainder.

What do you do if there is no term to subtract from in the dividend?

• Bring down the next term.

• Add a zero term.

• Multiply the divisor again.

• Start the division over.

What is the next step after bringing down the next term in the dividend?

• Multiply the new term by the divisor.

• Add the new term to the quotient.

• Divide the new term by the divisor.

• Subtract the new term from the quotient.

How do you handle the remainder in polynomial division?

• Ignore it.

• Multiply it by the divisor.

• Add it to the quotient.

• Express it as a fraction over the divisor.

What is the final form of the answer in polynomial long division?

• Quotient - Remainder

• Quotient - (Remainder/Divisor)

• Quotient + Remainder

• Quotient + (Remainder/Divisor)