The quotient of the provided polynomial divide by the (x+6) with the help of synthetic division method is,
![f(x)=4x^2-27x+167-\dfrac{996}{x+6}](https://tex.z-dn.net/?f=f%28x%29%3D4x%5E2-27x%2B167-%5Cdfrac%7B996%7D%7Bx%2B6%7D)
<h3>What is the factor of polynomial?</h3>
The factor of a polynomial is the terms in linear form, which are when multiplied together, give the original polynomial equation as result.
The polynomial given in the problem is,
![4x^3-3x^2+5x+6](https://tex.z-dn.net/?f=4x%5E3-3x%5E2%2B5x%2B6)
This polynomial is divided by the linear factor (x+6). Thus use -6 to for the synthetic division of polynomial as,
-6 | 4 -3 +5 6
x -24 +162 -1002
Add the numbers as,
4 -27 167 -996
Put these values, we get,
![f(x)=4x^2-27x+167-\dfrac{996}{x+6}](https://tex.z-dn.net/?f=f%28x%29%3D4x%5E2-27x%2B167-%5Cdfrac%7B996%7D%7Bx%2B6%7D)
Hence, the quotient of the provided polynomial divide by the (x+6) with the help of synthetic division method is,
![f(x)=4x^2-27x+167-\dfrac{996}{x+6}](https://tex.z-dn.net/?f=f%28x%29%3D4x%5E2-27x%2B167-%5Cdfrac%7B996%7D%7Bx%2B6%7D)
Learn more about factor of polynomial here;
brainly.com/question/24380382