Understanding Long Division of Polynomials

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

• Multiply the divisor by the dividend

• Identify the dividend and divisor

• Subtract the divisor from the dividend

• Add the divisor to the dividend

How do you determine what to multiply the divisor by in the first step of polynomial long division?

• By dividing the leading term of the dividend by the leading term of the divisor

• By adding the coefficients of the highest degree terms

• By subtracting the leading term of the divisor from the leading term of the dividend

• By multiplying the leading term of the divisor by the leading term of the dividend

What is the purpose of bringing the negative sign into each term during polynomial long division?

• To convert subtraction into addition

• To avoid errors in multiplication

• To make the division process faster

• To simplify the multiplication process

Why is it easier for the human brain to perform addition rather than subtraction during polynomial long division?

• Subtraction is less intuitive

• Addition is more straightforward

• Subtraction requires more steps

• Addition is more complex

What should you do after determining the number to multiply the divisor by in polynomial long division?

• Multiply it back into the divisor

• Divide it by the divisor

• Subtract it from the dividend

• Add it to the dividend

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

• Subtract the divisor from the expression

• Multiply the entire expression by the divisor

• Determine the next number to multiply the divisor by

• Add the divisor to the expression

How do you check if a polynomial long division has been done correctly?

• By ensuring the remainder has a lower degree than the divisor

• By ensuring the remainder is equal to the divisor

• By ensuring the remainder has a higher degree than the divisor

• By ensuring the remainder is larger than the divisor

What is the first way of writing a division statement after completing polynomial long division?

• Dividend equals divisor times quotient plus remainder

• Dividend equals remainder minus divisor times quotient

• Dividend equals divisor minus quotient plus remainder

• Dividend equals quotient times remainder plus divisor

What is the second way of writing a division statement after completing polynomial long division?

• Dividend divided by divisor equals remainder plus quotient over divisor

• Dividend divided by remainder equals divisor plus quotient over divisor

• Dividend divided by quotient equals divisor plus remainder over divisor

• Dividend divided by divisor equals quotient plus remainder over divisor

Why must the degree of the remainder be smaller than the degree of the divisor in polynomial long division?

• To ensure the division is complete

• To make the division process faster

• To simplify the multiplication process

• To avoid errors in subtraction