Question

How can I do this using

f(x) = x^2 + 8x + 16 and x - 4

Polynomial Division and the Remainder Theorem

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. x^2 + 8x + 16/x - 4

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

See below.

Explanation:

Part 1.

x + 12 <---------- Quotient.

------------------

x - 4 ( x^2 + 8x + 16

x^2- 4x

------------

12x + 16

12x - 48

----------

64 <--------- Remainder.

Part 2

f(4) = (4)^2 +8(4) + 16 = 16 + 32 + 16

= 64 Which is the remainder we found in the long division.

Part 3.

As you see in Parts 1 and 2, the Remainder Theorem tells you what the remainder is without doing the long division. If the remainder is 0 this means that the binomial you is a factor of the polynomial.