1. Splash Screen

2. You found the product of a sum and difference.
Factor perfect square trinomials.
Solve equations involving perfect squares.
Then/Now

3. Concept

4. 1. Is the first term a perfect square? Yes, 25x2 = (5x)2.
Recognize and Factor Perfect Square Trinomials
A. Determine whether 25x2 – 30x + 9 is a perfect square trinomial. If so, factor it.
1. Is the first term a perfect square? Yes, 25x2 = (5x)2.
2. Is the last term a perfect square? Yes, 9 = 32.
3. Is the middle term equal to 2(5x)(3)? Yes, 30x = 2(5x)(3).
Answer: 25x2 – 30x + 9 is a perfect square trinomial.
25x2 – 30x + 9 = (5x)2 – 2(5x)(3) + 32 Write as a2 – 2ab + b2.
= (5x – 3)2 Factor using the pattern.
Example 1

5. 1. Is the first term a perfect square? Yes, 49y2 = (7y)2.
Recognize and Factor Perfect Square Trinomials
B. Determine whether 49y2 + 42y + 36 is a perfect square trinomial. If so, factor it.
1. Is the first term a perfect square? Yes, 49y2 = (7y)2.
2. Is the last term a perfect square? Yes, 36 = 62.
3. Is the middle term equal to 2(7y)(6)? No, 42y ≠ 2(7y)(6).
Answer: 49y2 + 42y + 36 is not a perfect square trinomial.
Example 1

6. D. not a perfect square trinomial
A. Determine whether 9x2 – 12x + 16 is a perfect square trinomial. If so, factor it.
A. yes; (3x – 4)2
B. yes; (3x + 4)2
C. yes; (3x + 4)(3x – 4)
D. not a perfect square trinomial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Example 1

7. D. not a perfect square trinomial
B. Determine whether 49x2 + 28x + 4 is a perfect square trinomial. If so, factor it.
A. yes; (7x – 2)2
B. yes; (7x + 2)2
C. yes; (7x + 2)(7x – 2)
D. not a perfect square trinomial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Example 1

8. Concept

9. = 6(x + 4)(x – 4) Factor the difference of squares.
Factor Completely
A. Factor 6x2 – 96.
First, check for a GCF. Then, since the polynomial has two terms, check for the difference of squares.
6x2 – 96 = 6(x2 – 16) 6 is the GCF.
= 6(x2 – 42) x2 = x ● x and 16 = 4 ● 4
= 6(x + 4)(x – 4) Factor the difference of squares.
Answer: 6(x + 4)(x – 4)
Example 2

10. Factor Completely
B. Factor 16y2 + 8y – 15.
This polynomial has three terms that have a GCF of 1. While the first term is a perfect square, 16y2 = (4y)2, the last term is not. Therefore, this is not a perfect square trinomial.
This trinomial is in the form ax2 + bx + c. Are there two numbers m and p whose product is 16 ● (–15) or –240 and whose sum is 8? Yes, the product of 20 and –12 is –240, and the sum is 8.
Example 2

11. Find the factors of -240 (16 ● -15). Which pair adds to 8?
Factor Completely
16y2 + 8y – 15
Find the factors of -240 (16 ● -15). Which pair adds to 8?
-1 & & 40
-2 & & 30
-3 & & 24
-4 & & 20 Winner
-5 & & 16
(16y – 12)(16y + 20)
Factor out GCFs
4 (4y – 3) 4(4y + 5)
(4y – 3)(4y + 5)
Example 2

12. A. Factor the polynomial 3x2 – 3.
A. 3(x + 1)(x – 1)
B. (3x + 3)(x – 1)
C. 3(x2 – 1)
D. (x + 1)(3x – 3) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Example 2

13. B. Factor the polynomial 4x2 + 10x + 6.
A. (3x + 2)(4x + 6)
B. (2x + 2)(2x + 3)
C. 2(x + 1)(2x + 3)
D. 2(2x2 + 5x + 6) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Example 2

14. 4x2 + 36x = –81 Original equation
Solve Equations with Repeated Factors
Solve 4x2 + 36x = –81.
4x2 + 36x = –81 Original equation
4x2 + 36x + 81 = 0 Add 81 to each side.
(2x)2 + 2(2x)(9) + 92 = 0 Recognize 4x2 + 36x as a perfect square trinomial.
(2x + 9)2 = 0 Factor the perfect square trinomial.
(2x + 9)(2x + 9) = 0 Write (2x + 9)2 as two factors.
Example 3

15. 2x + 9 = 0 Set the repeated factor equal to zero.
Solve Equations with Repeated Factors
2x + 9 = 0 Set the repeated factor equal to zero.
2x = –9 Subtract 9 from each side.
Divide each side by 2.
Answer:
Example 3

16. Solve 9x2 – 30x + 25 = 0.
{0}
{-5} 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

17. Assignment
Page
Problems 12 – 26 & 34 – 42 (evens)
Skip #36