Polynomial division application question

Question

The remainder when (3x³ - 6x² + ax - 1) is divided by x-3 is the equal to the remainder obtained when the expression is divided by x + 1. Find the value of a. 

 

 

Answer 1

If f(x) = 3x³-6x²+ax-1, then, by the Remainder Theorem, f(3) is the remainder when f(x) is divided by x-3 and f(-1) is the remainder when f(x) is divided by x+1.

 

So, setting f(3) equal to f(-1), we have 81 - 54 + 3a - 1 = -3 - 6 - a - 1

 

                                                                        26 + 3a = -10 - a

 

                                                                               4a = -36

 

                                                                                 a = -9

 

Answer 2

Do the synthetic division with 3 in the 'slot' and save the remainder (it will involve a).

Do the synthetic division with -1 in the 'slot' and save this other remainder (involves a).

 

Set the two remainders equal, and solve that equation for a.