#f(x)=x^2-7x+4# and #c=2#? a. Evaluate f(c) directly? b. Evaluate f(c) using the Synthetic division and the Remainder Theorem? This a 2 part question and I need the equation with the answer

1 Answer
May 5, 2018

part a

Evaluate #f(c)# directly:

#f(c) = 2^2-7(2)+4#

#f(c) = -14#

part b

Evaluate #f(c)# using synthetic division and the remainder theorem:

What this is asking for is for you to perform the following division:

#x^2-7x+4 -: x - 2#

And show that the remainder is #-14#.

They are trying to make you good at doing synthetic division so I leave that exercise to you.

Also, they are trying to make you understand the concept that the remainder that you get when you divide a function by #x-a# is equal to the number that you get when you evaluate the function at #x = a#

When you do the long division, the remainder will be #-14#.