Question

algebra 2 with probability - i(a) - si
3 - 4: mathxl for school: practice and problem - sol
use synthetic division to divide.
\\(\frac{x^{3}+15x^{2}-2x - 14}{x + 1}\\)
\\(\frac{x^{3}+15x^{2}-2x - 14}{x + 1}=\square\\)
(simplify your answer. do not factor.)

Explanation:

Step1: Set up synthetic division

The divisor is $x + 1$, so we use $- 1$ (since $x+1 = 0$ gives $x=-1$). The coefficients of the dividend $x^{3}+15x^{2}-2x - 14$ are $1,15,-2,-14$.

Step2: Bring down the first - coefficient

Bring down the first coefficient $1$.

Step3: Multiply and add

Multiply $-1\times1=-1$, then add to the second coefficient: $15+( - 1)=14$.

Step4: Repeat the process

Multiply $-1\times14=-14$, then add to the third coefficient: $-2+( - 14)=-16$.

Step5: Multiply and add one more time

Multiply $-1\times(-16) = 16$, then add to the fourth coefficient: $-14 + 16=2$.
The quotient has coefficients $1,14,-16$ and the remainder is $2$. So the quotient is $x^{2}+14x-16$ with a remainder of $2$.

Answer:

$x^{2}+14x - 16+\frac{2}{x + 1}$