a. f(x)=x2-7x+4 --->f(c)=c2-7c+4
Replace c with 2 and solve.
b. The Remainder Theorem states that a polynomial, f(x), divided by a binomial, x-a, is the constant remainder, f(a).
That is: Dividend equals quotient times divisor plus remainder. Using synthetic division, we need to divide x2-7x+4 by
x-2. Because c=2 we need to do this:
2 1 -7 4
1 -5 -6<---This is your remainder which is your answer to f(c).
*Notice that both answers are the same, -6.