Question

I want to know if I'm on the right path or not, the answer I got was 2157; am I right or wrong, if not can someone help me??

Find each f(c) using synthetic substitution.
f(x) =5x^5+ 10x^4+ 3x^3+ 8x^2– 6x – 3; c = 3

Answer 1

f(3) = 2157

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.