Exercise 3 Page 177

Recall that we can use synthetic division as a compact way to calculate the division of a polynomial by a binomial of the form x-k. For this, we should follow some conventions to represent the division in a concise way. Let's review the conventions we take to identify the different parts of the polynomial division.

• The coefficients of the dividend should be written in order of descending exponents.
• We represent the divisor binomial x-k by writing the k-value to the left of the dividend polynomial.
• When the process is finished, the coefficients of the quotient can be found at the bottom row, and the last number is the remainder.

Following the conventions established above, we can identify the divisor binomial, the dividend polynomial, the quotient polynomial, and the remainder.

Finally, let's write the division being represented by the synthetic division provided. ( - 1)x^3 -2x^2 -9x+ 18÷ x-(- 3) = ( 1)x^2+( - 5)x + 6 ⇕ x^3-2x^2-9x+18÷ x+3 = x^2-5x+6