Dividing two polynomials using synthetic division

The video tutorial explains how to perform synthetic division on a polynomial. It begins by setting up the problem and identifying the zero of the divisor. The process of synthetic division is then demonstrated step-by-step, including bringing down coefficients, multiplying, and adding. The tutorial concludes by analyzing the remainder and writing the final quotient, highlighting that the divisor does not evenly divide the polynomial.

What is the first step in setting up a polynomial for synthetic division?

• Add the coefficients together

• Identify the highest degree term

• Set the divisor equal to zero

• Multiply all coefficients by two

When arranging the polynomial for synthetic division, what must be ensured about the coefficients?

• They are all negative

• They are in ascending order

• They are in descending order

• They are all positive

What is the result of adding -7 and 10 during the synthetic division process?

• 17

• -17

• -3

• 3

What does a remainder of 25 indicate in the context of synthetic division?

• The polynomial has no real roots

• The polynomial is a perfect square

• The divisor does not evenly divide the polynomial

• The divisor evenly divides the polynomial

How is the final quotient expressed after completing synthetic division?

• As a fraction with the remainder over the divisor

• As a single polynomial

• As a sum of squares

• As a product of two polynomials