Answer:
[tex]\frac{4x^3-3x^2+5x+6}{x+6}=4x^2-27x+167-\frac{996}{x+6}[/tex]
Step-by-step explanation:
The division problem given to us is [tex](4x^3-3x^2+5x+6)\div (x+6)[/tex].
To perform the synthetic division, we write out the coefficient of the polynomial. We set the linear factor to zero and solve for x, this becomes our divisor. That is [tex]x+6=0\implies x=-6[/tex].
We carry out the synthetic division as shown in the attachment.
The result of the synthetic division is 4 -27 167 -996
The first three terms are the coefficients of the quotient and the last term is the remainder.
Therefore the quotient is [tex]q(x)=4x^2-27x+167[/tex] and the remainder is [tex]r(x)=-996[/tex].
The dividend, the quotient and the divisor are written as
[tex]\frac{4x^3-3x^2+5x+6}{x+6}=4x^2-27x+167-\frac{996}{x+6}[/tex]
The correct answer is A
