Question

use synthetic division to divide the two polynomials. \\(\dfrac{-9w^5 - 18w^4 + 4w^3 + 21w^2 + 10w}{-3w - 5}\\) \
is the divisor given in \\((x - r)\\) form? no \
what do you need to multiply the divisor by to get a coefficient of 1? \\(\boldsymbol{-dfrac{1}{3}}\\) \
how many terms are in the dividend? 6 \
synthetic division table

Explanation:

Step1: Identify the divisor's leading coefficient

The divisor is \(-3w - 5\), and its leading coefficient is \(-3\).

Step2: Find the multiplier for leading coefficient 1

We want to make the leading coefficient of the divisor equal to \(1\). Let the multiplier be \(k\). So, \(k\times(-3)=1\). Solving for \(k\), we get \(k =-\frac{1}{3}\) (since \(-\frac{1}{3}\times(-3)=1\)).

Answer:

\(-\frac{1}{3}\)