Comparing Polynomial Long Division and Synthetic Division

What are the two methods mentioned for dividing polynomials?

• Long division and synthetic division

• Long division and short division

• Short division and synthetic division

• Synthetic division and polynomial division

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

• Drawing the division bar

• Writing the coefficients

• Multiplying the terms

• Subtracting the terms

In long division, what do you do after multiplying the divisor by the quotient term?

• Add the terms

• Multiply the terms again

• Subtract the terms

• Divide the terms

What is the key requirement for using synthetic division?

• The divisor must be a constant

• The divisor must be a polynomial

• The divisor must be in the form x - c

• The divisor must be in the form x + c

What do you write on the top of the synthetic division box?

• The divisor

• The remainder

• The coefficients of the polynomial

• The terms of the polynomial

In synthetic division, what do you do after multiplying the divisor by the current term?

• Subtract the result from the next coefficient

• Add the result to the next coefficient

• Multiply the result by the next coefficient

• Divide the result by the next coefficient

What is the final step in synthetic division?

• Dividing the terms

• Writing the quotient and remainder

• Subtracting the terms

• Multiplying the terms

What happens to the degree of the polynomial in the quotient after division?

• It decreases by one

• It increases by one

• It remains the same

• It doubles

What is the remainder when dividing x^4 - 3x - 1 by x + 2 using synthetic division?

• 19

• 21

• 20

• 22

Which method is faster but has limitations?

• Short division

• Polynomial division

• Long division

• Synthetic division