Question

Find each f(c) using synthetic substitution.f(x) = –x7 + 4x6 – 4x5 – 6x4 – 3x3 – 6x2 – x – 2; c = –5 1) 149,6032) –1,7923) –16,0224) –32,407

Answer 1

Consider that the remainder theorem states that when we divide a polynomial f(x)

by x-c, the remander R is equal to f(c).

Then, use synthetic division to find the remainder of f(x) divideby by x-c, with c=-5, as follow:

Use only the coefficient of f(x),

-1 4 -4 -6 -3 -6 -1 -2 l -5

5 -45 245 -1195 5990 -29920 149605

-1 9 -49 239 -1198 5984 29921 149603

The remainder is 149,603.

Then, you can conclude that the value of f(c) is:

f(-5) = 149,603