Learn how to divide using synthetic division with multiple zeros

The video tutorial explains how to perform synthetic division, particularly when the divisor is linear. It begins by comparing long division and synthetic division, highlighting the latter's simplicity for linear divisors. The instructor then demonstrates setting up the synthetic division process, emphasizing the importance of accounting for all polynomial terms, even those with zero coefficients. The steps of synthetic division are detailed, including bringing down the first term, multiplying diagonally, and adding vertically. The tutorial concludes by interpreting the result, identifying the quotient and remainder, and inviting questions.

What is the preferred method for dividing when the divisor is linear?

• Factoring

• Synthetic division

• Long division

• Polynomial expansion

Why do we rewrite the polynomial with missing terms included as zero coefficients?

• To ensure all place values are accounted for in synthetic division

• To change the degree of the polynomial

• To make the polynomial longer

• To simplify the polynomial

What is the first step in setting up synthetic division?

• Bring down the first term

• Divide the first term

• Add the coefficients

• Multiply the coefficients

What does a remainder of zero indicate in synthetic division?

• The divisor is not a factor

• The division is exact with no remainder

• The division is incorrect

• The polynomial is incomplete

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

• X to the 5th plus X to the 4th

• X to the 4th plus X^3 + X^2 + X + 1

• X^2 + X + 1

• X^3 + X^2 + X + 1