Question

`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

Answer 1

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`.