8-9 Perfect Square Trinomials

Example 1: Determine whether 16𝒏𝟐 – 24n + 9 is a perfect square trinomial. Then factor it.

Example 2: Determine whether 16𝒙𝟐– 32x + 15 is a perfect square trinomial. Then factor it.

Exercises Determine whether each trinomial is a perfect square trinomial. Write yes or no. If so, factor it.

1. 𝑥!– 16x + 64 2. 𝑚! + 10m + 25 3. 𝑝! + 8p + 64 Factor.

4. 98𝑥! – 200y2 5. 𝑥! + 22x + 121 6. 81 + 18j + j2 10. 16𝑚! + 48m + 36 11. 16 – 25𝑎! 12. 𝑏! – 16b + 256

Taking the Square Root

The square root of a number has positive and negative solutions.

𝑥! = 49 𝑦! = 64 2𝑎! + 2 = 164 𝑧! = −4

2𝑥 − 3 ! − 36 = 0 !!"𝑥! = 3

Finding the Zeros

Examples

a. 𝒙𝟐 – 6x + 9 = 0

b. (𝒂 − 𝟓)𝟐 = 64

Exercises 1. 𝑥! + 4x + 4 = 0 2. 16𝑛! + 16n + 4 = 0 3. 𝑝! + 2p + 1 = 49 4. (𝑥 + 3)! = 49

Homework Problems:

(p. 526) #11*, 13-25 odd, 29, 33, 38-40, 44*. 45*, 65, 67, 73 Remember Vertical Motion Equation: ℎ = −16𝑡!

+ 𝑣!𝑡 + ℎ! (if no 𝑣! 𝑖𝑠 𝑔𝑖𝑣𝑒𝑛, 𝑎𝑠𝑠𝑢𝑚𝑒 𝑖𝑡 𝑖𝑠 0)