Question 177074
You need to use polynomial long division to divide {{{x^3 + cx + d}}} by {{{x + 1}}}.  Remember to include the missing {{{x^2}}} term, so your dividend becomes {{{x^3 + 0x^2 + cx + d}}}.   Rendering polynomial long division on this site is very difficult, so I'm just going to hope you know how to do that.  You will find that the remainder is {{{d - (c + 1)}}} which you are told is equal to 3.


Do the polynomial long division again, this time using {{{x - 2}}} as a divisor and you will discover that the remainder is {{{d + 2(c + 4)}}} which you are told is equal to -3.


Now you have two 2-variable linear equations:


{{{d - c - 1 = 3}}} => {{{d - c = 4}}} and


{{{d + 2c + 8 = -3}}} => {{{d + 2c = -11}}}


Solve this system for c and d to get your answer.