use the long division method to find the result when $4x^{3}+20x^{2}+19x + 18$ is divided by $x + 4$. if…

use the long division method to find the result when $4x^{3}+20x^{2}+19x + 18$ is divided by $x + 4$. if there is a remainder, express the result in the form $q(x)+\frac{r(x)}{b(x)}$.

use the long division method to find the result when $4x^{3}+20x^{2}+19x + 18$ is divided by $x + 4$. if there is a remainder, express the result in the form $q(x)+\frac{r(x)}{b(x)}$.

Answer

Explanation:

Step1: Divide leading terms

Divide $4x^{3}$ by $x$. We get $4x^{2}$. [ \begin{align*} 4x^{2}(x + 4)&=4x^{3}+16x^{2}\ (4x^{3}+20x^{2}+19x + 18)-(4x^{3}+16x^{2})&=4x^{2}+19x+18 \end{align*} ]

Step2: Divide new leading term

Divide $4x^{2}$ by $x$. We get $4x$. [ \begin{align*} 4x(x + 4)&=4x^{2}+16x\ (4x^{2}+19x + 18)-(4x^{2}+16x)&=3x+18 \end{align*} ]

Step3: Divide new leading term

Divide $3x$ by $x$. We get $3$. [ \begin{align*} 3(x + 4)&=3x+12\ (3x + 18)-(3x+12)&=6 \end{align*} ]

Answer:

$4x^{2}+4x + 3+\frac{6}{x + 4}$