Create a quadratic polynomial function f(x) and a linear binomial in the form (x − a).

Question

Part 1. Show all work using long division to divide your polynomial by the binomial.
Part 2. Show all work to evaluate f(a) using the function you created.
Part 3. Use complete sentences to explain how the remainder theorem is used to determine whether your linear binomial is a factor of your polynomial function

Answer 1

What have you got so far for this assignment?
You didn't expect me to just do it for you, did you?

Answer 2

I do not understand this question.

Answer 3

suppose we have
f(x) = 3x^3 - 5x^2 + 4x + 1
and we divide that by x-2
( I can't show the long algebraic division in this format, but I am sure you know how to do that)

you should have 3x^2 + x + 6 with a remainder of 13

now let's find f(2)
f(2) = 3(8) - 5(4) + 4(2) + 1
= 24 - 20 + 8 + 1
= 13

What would happen if the remainder is zero?
Wouldn't your original expression factor?

So as long as f(a) gives you a non-zero result, you know that the expression would NOT factor,
conversely .....