identify the polynomial divisor, dividend, and quotient represented by the synthetic division. -3 | 2 11 18…

Explanation:

Step1: Recall synthetic - division rule

In synthetic division, if we have the form $x - c$ for the divisor, the number outside the synthetic - division box is $c$. Here, the number outside is $- 3$, so the divisor is $x+3$ (since $x-(-3)=x + 3$).

Step2: Determine the dividend

The coefficients of the polynomial in the dividend are the numbers on the top row of the synthetic - division setup. The coefficients are $2,11,18,9$, which correspond to the polynomial $2x^{3}+11x^{2}+18x + 9$.

Step3: Find the quotient

The numbers in the bottom row (excluding the last remainder) give the coefficients of the quotient polynomial. The coefficients of the quotient are $2,5,3$, which correspond to the polynomial $2x^{2}+5x + 3$.

Answer:

Divisor: x + 3 Dividend: $2x^{3}+11x^{2}+18x + 9$ Quotient: $2x^{2}+5x + 3$