Dividing Polynomials with Synthetic Division

The video tutorial explains synthetic division, emphasizing the need for the divisor to be a linear factor in the form of x minus k. It outlines the process of setting up synthetic division by listing coefficients in descending order and describes the algorithm, which involves multiplying diagonals and adding vertically. The tutorial concludes by comparing synthetic division to long division, highlighting its simplicity and specific applicability.

What is the required form of the divisor in synthetic division?

• x^2 - k

• x - k

• x + k

• k - x

Why can't the divisor have an x^2 term in synthetic division?

• Because it would not be a linear factor

• Because it would be too complex

• Because it would be a monomial

• Because it would be a constant

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

• Repeat the previous term

• Add a one for the missing term

• Add a zero for the missing term

• Ignore the missing term

What is the first step in the synthetic division algorithm?

• Add the coefficients

• Multiply the coefficients

• Set the divisor equal to zero

• Bring down the first coefficient

In synthetic division, what operation is performed after multiplying the diagonal?

• Square the result

• Subtract the result

• Add the result

• Divide the result

What is the result of 3 times 2 in the synthetic division example?

• 5

• 6

• 8

• 7

What is the remainder in synthetic division if the last number is zero?

• The remainder is the first coefficient

• The remainder is the last coefficient

• The remainder is one

• The remainder is zero

What is the final answer format in synthetic division?

• Remainder, constant, linear, quadratic

• Constant, linear, quadratic, remainder

• Quadratic, linear, constant, remainder

• Linear, quadratic, constant, remainder

When can synthetic division be applied?

• When the divisor is a constant

• When the divisor is a linear binomial

• When the divisor is a quadratic binomial

• When the divisor is a monomial

What is the final polynomial result in the given synthetic division example?

• 3x^2 - 2x + 7

• 3x^2 + 2x - 7

• 2x^2 + 3x - 7

• 2x^2 - 3x + 7