use synthetic division to solve $(4x^{3}-3x^{2}+5x + 6)div(x + 6)$. what is the quotient?\n$4x^{2}-27x +…

use synthetic division to solve $(4x^{3}-3x^{2}+5x + 6)div(x + 6)$. what is the quotient?\n$4x^{2}-27x + 167-\frac{996}{x - 6}$\n$4x^{2}+21x + 131+\frac{792}{x + 6}$\n$4x^{2}+21x + 131+\frac{792}{x - 6}$\n$4x^{2}-27x + 167-\frac{996}{x + 6}$

use synthetic division to solve $(4x^{3}-3x^{2}+5x + 6)div(x + 6)$. what is the quotient?\n$4x^{2}-27x + 167-\frac{996}{x - 6}$\n$4x^{2}+21x + 131+\frac{792}{x + 6}$\n$4x^{2}+21x + 131+\frac{792}{x - 6}$\n$4x^{2}-27x + 167-\frac{996}{x + 6}$

Answer

Explanation:

Step1: Set up synthetic division

For $(4x^{3}-3x^{2}+5x + 6)\div(x + 6)$, we use - 6 (since $x+6=x-(-6)$) in the synthetic - division setup. The coefficients of the dividend are 4, - 3, 5, 6.

Step2: Bring down the first coefficient

Bring down the first coefficient 4.

Step3: Multiply and add

Multiply - 6 by 4 to get - 24. Add - 24 to - 3: $-3+( - 24)=-27$.

Step4: Multiply and add again

Multiply - 6 by - 27 to get 162. Add 162 to 5: $5 + 162=167$.

Step5: Multiply and add one more time

Multiply - 6 by 167 to get - 1002. Add - 1002 to 6: $6+( - 1002)=-996$. The quotient is $4x^{2}-27x + 167$ and the remainder is - 996. So the result of the division is $4x^{2}-27x + 167-\frac{996}{x + 6}$.

Answer:

$4x^{2}-27x + 167-\frac{996}{x + 6}$