1. Factoring Polynomials by Completing the Square

2. Perfect Square Trinomials
Examples
x2 + 6x + 9
x2 - 10x + 25
x2 + 12x + 36

3. Creating a Perfect Square Trinomial
In the following perfect square trinomial, the constant term is missing X2 + 14x + ____
Find the constant term by squaring half the coefficient of the linear term.
(14/2) X2 + 14x + 49

4. Perfect Square Trinomials
Create perfect square trinomials.
x2 + 20x + ___
x2 - 4x + ___
x2 + 5x + ___
100 4
25/4

5. Factoring Quadratics by Completing the Square
Factor by completing the square:
Step 1: First take the coefficient of the linear term, divide it by 2, and then square it. This gives 16 - (8/2)2

6. What if a is NOT 1
3x2 + 6x + c
2x2 + 5x + c

7. Factoring by Completing the Square
Step 2: Add and subtract 16 just after the linear term. Therefore, you did not change the value of the expression.

8. Factoring by Completing the Square
Step 3: Use brackets to group the first three terms – This is your perfect square trinomial.

9. Factoring by Completing the Square
Step 3: Factor the perfect square trinomial and simplify the rest.
(x + 4)2 + 4

10. X2 – 12x + 4
Step 1: First take the coefficient of the linear term, divide it by 2, and then square it.
Step 2: Add and subtract 16 just after the linear term. Therefore, you did not change the value of the expression.
Step 3: Use brackets to group the first three terms – This is your perfect square trinomial.

11. Factor by Completing the Square
Step 1: First take the coefficient of the linear term, divide it by 2, and then square it.
Step 2: Add and subtract this value.
Step 3: Use brackets to group the first three terms – This is your perfect square trinomial.

12. Factoring by Completing the Square

13. Factoring by Completing the Square
Try the following examples. Do your work on your paper.