Learn the basics of applying synthetic division to divide two polynomials

The video tutorial introduces synthetic division as an alternative to long division for polynomials. It explains the conditions under which synthetic division can be used, specifically when the divisor is a linear binomial. The instructor provides a step-by-step guide on setting up and executing synthetic division, emphasizing the importance of identifying the zero of the divisor. The tutorial concludes with an explanation of how to interpret the results, including identifying the remainder, constant, linear, and quadratic terms in the quotient.

What is a necessary condition for using synthetic division?

• The dividend must be a constant.

• The divisor must be a linear binomial.

• The divisor must have a degree of 2.

• The divisor must be a quadratic polynomial.

How do you determine the zero of the divisor in synthetic division?

• By multiplying the coefficients.

• By solving the divisor equation for zero.

• By adding the coefficients.

• By subtracting the coefficients.

In synthetic division, what is the first step after setting up the coefficients?

• Add the coefficients vertically.

• Divide the coefficients by the zero.

• Multiply the first coefficient by the zero.

• Subtract the coefficients diagonally.

What operation is performed on the diagonal in synthetic division?

• Addition

• Subtraction

• Division

• Multiplication

What does the first number in the result of synthetic division represent?

• The quadratic term

• The linear term

• The remainder

• The constant term

Which term follows the quadratic term in the result of synthetic division?

• Cubic term

• Linear term

• Remainder

• Constant term

What is the final quotient obtained from the synthetic division in the example?

• 2X^2 - X + 3

• X^2 + 2X + 3

• X^2 + X + 2

• 2X^2 + X + 3