Respuesta :
The quotient of the provided polynomial divide by the (x+6) with the help of synthetic division method is,
[tex]f(x)=4x^2-27x+167-\dfrac{996}{x+6}[/tex]
What is the factor of polynomial?
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,
[tex]4x^3-3x^2+5x+6[/tex]
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,
[tex]f(x)=4x^2-27x+167-\dfrac{996}{x+6}[/tex]
Hence, the quotient of the provided polynomial divide by the (x+6) with the help of synthetic division method is,
[tex]f(x)=4x^2-27x+167-\dfrac{996}{x+6}[/tex]
Learn more about factor of polynomial here;
https://brainly.com/question/24380382
