1. 2.8 Warm Up Factor. 1.8x² + 26x + 15 2.2x² + 15x + 7 3.5x² - 18x - 8

2. 2.8 Factor Special Products

3. EXAMPLE 1 Factor the difference of two squares Factor the polynomial. a. y 2 – 16 = b. 25m 2 – 36 c. x 2 – 49y 2

4. EXAMPLE 2 Factor the difference of two squares Factor the polynomial 8 – 18n 2. 8 – 18n 2 = 2(4 – 9n 2 ) = 2(2 + 3n)(2 – 3n) Factor out common factor. Difference of two squares pattern

5. GUIDED PRACTICE for Examples 1 and 2 Factor the polynomial. 1. 4y 2 – 64 = (2y + 8)(2y – 8)

6. EXAMPLE 3 Factor perfect square trinomials Factor the polynomial. a.a. n 2 – 12n + 36 b.b. 9x 2 – 12x + 4 c.c. 4s 2 + 4st + t 2

7. EXAMPLE 4 Factor a perfect square trinomial Factor the polynomial –3y 2 + 36y – 108. –3y 2 + 36y – 108 Factor out –3. = –3(y – 6) 2 Perfect square trinomial pattern = –3(y 2 – 12y + 36)

8. GUIDED PRACTICE for Examples 3 and 4 Factor the polynomial. = (h + 2) 2 2. h 2 + 4h + 4 3. 2y 2 – 20y + 50 = 2(y – 5) 2 4. 3x 2 + 6xy + 3y 2 = 3(x + y) 2

9. EXAMPLE 5 Solve a polynomial equation Solve the equation x 2 + + = 0. 2 3 x 1 9 Write original equation. 9x2 + 6x + 1 = 09x2 + 6x + 1 = 0 Multiply each side by 9. (3x + 1) 2 = 0 x = – 1 3 Solve for x. x 2 + + = 0 1 9 2 3 x ANSWER The solution of the equation is –. 1 3

10. GUIDED PRACTICE for Examples 5 and 6 Solve the equation 5. a 2 + 6a + 9 = 0 a = –3 6. w 2 – 14w + 49 = 0 w = 7 7. n 2 – 81= 0 n = – 9 or n = 9

11. FALLING OBJECT SOLUTION EXAMPLE 6 Solve a vertical motion problem A window washer drops a wet sponge from a height of 64 feet. After how many seconds does the sponge land on the ground ? Use the vertical motion model to write an equation for the height h (in feet) of the sponge as a function of the time t (in seconds) after it is dropped.

12. EXAMPLE 6 Solve a vertical motion problem The sponge was dropped, so it has no initial vertical velocity. Find the value of t for which the height is 0. h = –16t 2 + vt + s Vertical motion model 0 = –16t 2 + (0)t + 64 Substitute 0 for h, 0 for v, and 64 for s. 0 = –16(t 2 – 4) Factor out –16. 0 = –16(t – 2)(t +2) Difference of two squares pattern t – 2 = 0 or t + 2 = 0 Zero-product property t = 2 or t = –2 Solve for t. Disregard the negative solution of the equation. ANSWER The sponge lands on the ground 2 seconds after it is dropped.