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

use synthetic division to solve $(4x^{3}-3x^{2}+5x + 6)+(x + 6)$. 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 $(4x^{3}-3x^{2}+5x + 6)+(x + 6)$. 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 (x=-6). The coefficients are (4,-3,5,6).

Step2: Bring down the first coefficient

Bring down (4).

Step3: Multiply and add

Multiply (4) by (-6) to get (-24). Add (-3+(-24)=-27). Multiply (-27) by (-6) to get (162). Add (5 + 162=167). Multiply (167) by (-6) to get (-1002). Add (6+(-1002)=-996). The quotient polynomial is (4x^{2}-27x + 167) and the remainder is (-996). So (\frac{4x^{3}-3x^{2}+5x + 6}{x + 6}=4x^{2}-27x+167-\frac{996}{x + 6})

Answer:

(4x^{2}-27x + 167-\frac{996}{x + 6}) (the fourth option)