Question

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

Explanation:

Step1: Analyze the divisor's coefficient

The divisor is \(-3w - 5\). We want the coefficient of \(w\) to be \(1\). Let the multiplier be \(k\). So \(k\times(-3w - 5)=w + \frac{5}{3}\) (we want the coefficient of \(w\) to be \(1\)). Solving for \(k\) in the coefficient of \(w\): \(k\times(-3)=1\), so \(k =-\frac{1}{3}\).

Step2: Count the terms in the dividend

The dividend is \(-9w^{5}-18w^{4}+4w^{3}+21w^{2}+10w\). Let's list the terms: \(-9w^{5}\), \(-18w^{4}\), \(4w^{3}\), \(21w^{2}\), \(10w\). So there are 5 terms.

Answer:

To get a coefficient of 1 for \(w\) in the divisor, we multiply by \(-\frac{1}{3}\). The number of terms in the dividend is 5.