Answer:
f(3) = 2157
Step-by-step explanation:
Finding the remainder using synthetic division is essentially equivalent to evaluating the following using x=3:
f(x) = ((((5x +10)x +3)x +8)x -6)x -3
f(3) = ((((5·3 +10)3 +3)3 +8)3 -6)3 -3
= (((25·3 +3)3 +8)3 -6)3 -3
= ((78·3 +8)3 -6)3 -3
= (242·3 -6)3 -3
= 720·3 -3
= 2157
Your answer looks right to me.
