Question

use synthetic division to divide the two polynomials.$w-5overline{)-5w^{3}+29w^{2}-15w-44}$is the divisor given in $(x - r)$ form? yeshow many terms are in the dividend?enter the quotient and remainder.quotient+remaindersynthetic division table

Explanation:

Step1: Count dividend terms

The dividend is $-5w^3 + 29w^2 - 15w - 44$, which has 4 terms.

Step2: Identify $r$ for synthetic division

Divisor is $w-5$, so $r=5$. List dividend coefficients: $-5, 29, -15, -44$.

Step3: Perform synthetic division

$$\begin{array}{r|rrrr} 5 & -5 & 29 & -15 & -44 \\ & & -25 & 20 & 25 \\ \hline & -5 & 4 & 5 & -19 \\ \end{array}$$

Step4: Define quotient and remainder

The first 3 values are quotient coefficients (degree 2): $-5w^2 + 4w + 5$. Last value is remainder: $-19$.

Answer:

Number of terms in dividend: 4
Quotient: $\boldsymbol{-5w^2 + 4w + 5}$
Remainder: $\boldsymbol{-19}$