Question

Find each f(c) using synthetic substitution.f(x) = –x^7 + 4x^6 – 4x^5 – 6x^4 – 3x^3 – 6x^2 – x – 2; c = –5 1) 149,6032) -1,7923) -16,0224) -32,407

Answer 1

We need to use synthetic substitution to find f(-5):

First, we need to write -5 followed by the coefficients of each monomial:

-5 | -1 4 -4 -6 3 -6 -1 -2

Then, we keep the first coefficient and write it again under itself:

-5 | -1 4 -4 -6 3 -6 -1 -2

-1

Then, we sum we multiply -5 by the first number on the second row, and write the result (-5 * (-1) = 5) under the second coefficient:

-5 | -1 4 -4 -6 3 -6 -1 -2

-1 5

Then, we multiply -5 by the second number on the second row, and place the result (-5 * 5 = -25) under the third coefficient:

-5 | -1 4 -4 -6 3 -6 -1 -2

-1 5 25

Then, we repeat this process for the other coefficients:

-5 * 25 = 1252

-5 | -1 4 -4 -6 3 -6 -1 -2

-1 5 25 125

-5 * 125 = -625