Dividing Polynomials with Synthetic Division

What is the prerequisite form for the binomial divisor in synthetic division?

• x^2 + ax + b

• x - a

• ax^2 + bx + c

• ax + b

In synthetic division, what should you do with the coefficients of the polynomial?

• Add them together

• Multiply them by the divisor

• Write them in a row

• Ignore them

What is the first step in the synthetic division process?

• Subtract the coefficients

• Multiply the coefficients

• Bring down the first coefficient

• Add the coefficients

In the first example, what is the remainder when x^3 + 2x^2 - 17x + 18 is divided by x - 2?

• 0

• 18

• -17

• 2

How can you verify the result of synthetic division?

• By adding the quotient and the divisor

• By dividing the quotient by the divisor

• By subtracting the quotient from the divisor

• By multiplying the quotient by the divisor and adding the remainder

What should you do if a term is missing in the polynomial during synthetic division?

• Ignore the missing term

• Use a placeholder zero

• Add a random coefficient

• Subtract the missing term

In the second example, what is the placeholder for the missing x^2 term?

• 0

• 2

• -1

• 1

What is the quotient when 2x^4 + 8x^3 + x + 4 is divided by x + 4?

• 2x^4 + 1

• 2x^3 + 4

• 2x^3 + 1

• 2x^4 + 4

In the final example, what is the leading term of the quotient when 3x^4 + 21 is divided by x + 7?

• 3x^3

• 3x^4

• 3x^2

• 3x

What is the remainder when 3x^4 + 21 is divided by x + 7?

• 35

• -5

• 0

• 21