Question

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

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

quadratic polynomial x^2 - x - 6 = f(x)
binomial (x-3)

dividing:-
x + 2
----------------------
x - 3 ) x^2 - x - 6
x^2 - 3x
----------
2x - 6
2x - 6
--------
.........

result of division is (x + 2)
s o we can write the function as (x - 3)(x + 2)

Part 2 f(a) = f(3) = (3)^2 - 3 - 6 = 0

Part3 The remainder Theorem states that the remainder when a polynomial is divided by (x - a) then the remainder is f(a). If f(a) = 0 then x - a is a factor.
In the above case f(3) = 0 therefore (x - 3) is a factor of our polynomial.