1. PERFECT SQUARE TRINOMIALS
Any trinomial of the form ax2 + bx + c that can be factored to be a (BINOMIAL Factor) squared
Sum Factors:
a2 + 2ab + b2 = (a + b)2
Difference Factors:
a2 - 2ab + b2 = (a - b)2
(1) 9x2 + 12x + 4
(2) x2 - 8x + 16
(3) 4x2 - 20x + 25
(4) x2 + 20x + 100

2. How do you make a perfect square trinomial?
STEP 1: DIVIDE middle term value (b-value) by 2
STEP 2: SQUARE it
STEP 3: Make your step 2 answer the constant
FACTORS:
Binomial is add if middle term is positive
Binomial is subtract if middle term is negative
EXAMPLE: x2 + 6x + c
EXAMPLE: x2 - 10x + c
Middle term: 6
Middle term: -10
Divide by 2: 3
Divide by 2: -5
Squared = 9
Squared = 25
x2 + 6x + 9 = (x + 3)2
x2 – 10x + 25 = (x - 5)2

3. Create Perfect Square Trinomials Practice finding “c”
x2 - 8x + c
x2 + 10x + c
x2 - 3x + c
x2 + 9x + c

4. Continued: Practice finding “c”

5. STEPS for COMPLETING THE SQUARE
ax2 + bx + c = 0
Step 1: Lead coefficient of x2 must be 1
DIVIDE by “a” value
Step 2: Subtract current ‘c’ term
Step 3: Find value to make a perfect square trinomial
Divide middle term, “bx”, by 2 and square
Add that value to both sides of equation
Step 4: Factor (perfect square!)
*Shortcut = half of middle term is part of binomial factor*
Step 5: Solve for x

6. Example: Solve by completing the square
x2 + 6x + 4 = 0
- SUBTRACT 4
x2 + 6x = - 4
Find the constant value to create a perfect square and ADD to both sides
(half of 6 is 3, 3 squared is 9)
-FACTOR perfect square trinomial
x2 + 6x + 9 =
(x + 3)2 = 5
SOLVE for x: Square root both sides Use plus or minus (Check to simplify radical)

7. Practice #1: Completing the Square1. 2. 3. 4.

8. Example with leading coefficient
- Divide every number by 2
- Add 3/2 on both sides
Find c to make perfect square trinomial
(half of 2 = 1, 1 squares = 1
- Factor left side, combine like terms on the right
- Solve for x:
Square Root with plus/minus
Rationalize Fraction Radicals

9. Practice #2: Completing the Square2. 1. 3. 4.
Math 3 Hon: Unit 3

10. Practice: Equations with Complex Solutions1. 2. 3. 4.

11. Practice : Solve Equations to equal zero?1. 2.

12. 3. 4.