Lesson 6-3 Synthetic Division

Step 1:
Copy the Standard(s) and Essential Question(s) into your spiral notebook.

Standard(s):
A.APR.2 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) =0 if and only if (x – a) is a factor of p(x).

Essential Question(s):
What goes in the top left corner when using Synthetic Division?
What do you have to remember if a polynomial term is missing?
What is the next step, after Synthetic Division,that is necessary to find the other zeros?

Step 2:
Make sure you can define and identify the following terms as you go through the next 2 lessons.

Step 3:
Watch the video on Synthetic Division.

Step 4:
Example with Synthetic Division and Factoring Completely

• Put a in the top left corner!
• Use the coefficients of the polynomial in standard form!
• Place a zero for any missing terms!
• Perform the Division Technique!

• Write the polynomial that is left using the coefficients that are at the bottom!

• Factor Completely!

• Use the Zero Product Property to find the zeros!

In the example above:

Notice the result, and the fact that it is zero! So evaluating the function for 4 is the same as performing Synthetic Division. The remainders are identical. That's what the Remainder Theorem is trying to say.

Step 5:
Do you OWN it ?

Take Lesson 6-3 Quiz.