Question

Please help... I really need this.

Answer 1

`(4x^3-3x^2+5x+6)/(x+6)=4x^2-27x+167-(996)/(x+6)`

Explanation:

The division problem given to us is
`(4x^3-3x^2+5x+6)/ (x+6)`.

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
`x+6=0\implies x=-6`.

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
`q(x)=4x^2-27x+167` and the remainder is
`r(x)=-996`.

The dividend, the quotient and the divisor are written as

`(4x^3-3x^2+5x+6)/(x+6)=4x^2-27x+167-(996)/(x+6)`

The correct answer is A