Question 747975
{{{3x^3 - 15x^2 -42x}}} ..........
First, factor this, and then you have a simpler dividend to use.
{{{3x^3 - 15x^2 -42x = 3x*(x^2-5x-14)}}}


Now, you would do the division of {{{(x^2-5x-14)/(x+2)}}}, and then put back your factor of 3x.


The root being tested would be -2, so set up the synthetic div.


-2____|____1____-5____-14
______|
______|_________-2_____14
___________________________
___________1____-7_____0     Remainder is 0


This means, QUOTIENT IS {{{1*x-7}}}, or {{{highlight(x-7)}}}.  According to the original expression to be divided, the quotient of that would be {{{3x(x-7)=highlight(3x^2-21)}}}