Question 925497
Express {{{f(x)}}} in the form {{{f(x)=(x-k)q(x)+r}}} for the given value {{{k}}}:


{{{f(x)=3x^4-2x^3-15x^2-x}}}; {{{k=4}}}

{{{f(x)=(x-___)(___)+_____}}}


write down coefficients:

3){{{3}}}...{{{-2}}}...{{{-15}}}...{{{-1}}}... {{{0}}}  -> multiply by {{{k=4}}}
. ___{{{12}}}___{{{40}}}__{{{100}}}__{{{396}}}___add  
. {{{3}}}. .{{{10}}}.... . {{{25}}}.....{{{ 99}}}.....{{{ 396}}} <== remainder "r"

 coefficients for {{{q(x)}}}
{{{3}}}. .{{{10}}}. .... {{{25}}}..... {{{99}}}.... {{{396}}} means 

{{{q(x) = 3x^3 + 10x^2 + 25x + 99}}}

{{{f(x) = (x - 4)(3x^3 + 10x^2 + 25x + 99) + 396}}} <==ANSWER