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3 years ago

Please help... I really need this.

Mathematics

1 answer:

valentinak56 [21]3 years ago

3 0

Answer:

$\frac{4x^3-3x^2+5x+6}{x+6}=4x^2-27x+167-\frac{996}{x+6}$

Step-by-step explanation:

The division problem given to us is $(4x^3-3x^2+5x+6)\div (x+6)$ .

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

$\frac{4x^3-3x^2+5x+6}{x+6}=4x^2-27x+167-\frac{996}{x+6}$

The correct answer is A

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