The document discusses the concept of squares and how to complete the square in quadratic expressions. It uses algebra tiles to demonstrate how to factor non-factorable problems into perfect squares. Additionally, it includes exercises on determining the necessary values to complete the square for various equations.

3. What does a square look like?
Is this a square?
What about this one?
This one?
Why isn’t the last picture a square?
What would we need to do to make this a
square?

4. We can model a quadratic expression like this
x2
+ 4x + 4 with tiles like this

5. We are missing a space in our square.
Illustrative Example:
x2
+ 6x – 8 = 0
We will use algebra tiles to help us with the non factorable problem.
The algebra tiles will help us get a new c value that will help us
factor into a new perfect square.
ax2
+ bx + c
a= b = c =
so for x2
+ 6x – 8 ; a = 1 b = 6 c = -8
using algebra tiles we have
How many s would we really need to complete the square?
Answer = 9 s

6. A. Complete the square of the following:
1. x² + 4x + _____
2. x² – 6x + _____
3. x² – 12 x +_____
4. n² – 18n + _____
5. x² + 8x + _____

7. B. Determine a number that must be added
to both sides of each equation to complete
the square?
1. x2
+ 4x = 12
2. x2
– 2x = 24
3. x2
– 6x = -8
4. x2
– 6x = 7
5. x2
+ 6x = 16

8. 1.What does it mean to “complete the square”?
2.How do you describe a perfect square
trinomial?
3.How can you determine a number that must be
added to the terms of polynomial to make it a
perfect square trinomial?
4.Observe the terms of each trinomial. How is the
third term related to the coefficient of the middle
term?