1. Factoring Special Cases
ALGEBRA 1 LESSON 7-7
Factor m2 – 6m + 9.
m2 – 6m + 9 = m • m – 6m + 3 • 3 Rewrite first and last terms.
= m • m – 2(m • 3) + 3 • 3 Does the middle term equal 2ab? 6m = 2(m • 3)
= (m – 3)2 Write the factors as the square of a binomial.
7-7

2. Factoring Special Cases
ALGEBRA 1 LESSON 7-7
The area of a square is (16h2 + 40h + 25) in.2. Find the length of a side.
16h2 + 40h + 25 = (4h)2 + 40h + 52 Write 16h2 as (4h)2 and 25 as 52.
= (4h)2 + 2(4h)(5) + 52 Does the middle term equal 2ab? 40h = 2(4h)(5)
= (4h + 5)2 Write the factors as the square of a binomial.
The side of the square has a length of (4h + 5) in.
7-7

3. Factoring Special Cases
ALGEBRA 1 LESSON 7-7
Factor a2 – 16.
a2 – 16 = a2 – 42 Rewrite 16 as 42.
= (a + 4)(a – 4) Factor.
Check: Use FOIL to multiply.
(a + 4)(a – 4)
a2 – 4a + 4a – 16
a2 – 16
7-7

4. Factoring Special Cases
ALGEBRA 1 LESSON 7-7
Factor 9b2 – 25.
9b2 – 225 = (3b)2 – 52 Rewrite 9b2 as (3b)2 and 25 as 52.
= (3b + 5)(3b – 5) Factor.
7-7

5. Factoring Special Cases
ALGEBRA 1 LESSON 7-7
Factor 5x2 – 80.
5x2 – 80 = 5(x2 – 16) Factor out the GCF of 5.
= 5(x + 4)(x – 4) Factor (x2 – 16).
Check: Use FOIL to multiply the binomials. Then multiply by the GCF.
5(x + 4)(x – 4)
5(x2 – 16)
5x2 – 80
7-7

6. = (2x + 1)(3x2 – 2) Factor out (2x + 1).
Factoring by Grouping
ALGEBRA 1 LESSON 7-7
Factor 6x3 + 3x2 – 4x – 2.
6x3 + 3x2 – 4x – 2 = 3x2(2x + 1) – 2(2x + 1) Factor the GCF from each group of two terms.
= (2x + 1)(3x2 – 2) Factor out (2x + 1).
= 6x3 – 4x + 3x2 – 2 Use FOIL.
Check: 6x3 + 3x2 – 4x – (2x + 1)(3x2 – 2)
= 6x3 + 3x2 – 4x – 2 Write in standard form.
7-7

7. 8t4 + 12t3 + 16t + 24 = 4(2t4 + 3t3 + 4t + 6) Factor out the GCF, 4.
Factoring by Grouping
ALGEBRA 1 LESSON 7-7
Factor 8t4 + 12t3 + 16t + 24.
8t4 + 12t3 + 16t + 24 = 4(2t4 + 3t3 + 4t + 6) Factor out the GCF, 4.
= 4[t3(2t + 3) + 2(2t + 3)] Factor by grouping.
= 4(2t + 3)(t3 + 2) Factor again.
7-7

8. Step 1: 24h2 + 10h – 6 = 2(12h2 + 5h – 3) Factor out the GCF, 2.
Factoring by Grouping
ALGEBRA 1 LESSON 7-7
Factor 24h2 + 10h – 6.
Step 1: 24h2 + 10h – 6 = 2(12h2 + 5h – 3)   Factor out the GCF, 2.
Step 2: 12 • –3 = –36 Find the product ac.
Step 3: Factors Sum
–2(18) = –36 – = 16
–3(12) = –36 – = 9
–4(9) = –36 –4 + 9 = 5
Find two factors of ac that have a sum b. Use mental math to determine a good place to start.
Step 4:  12h2 – 4h + 9h – 3 Rewrite the trinomial.
Step 5:   4h(3h – 1) + 3(3h – 1) Factor by grouping.
  (4h + 3)(3h – 1) Factor again.
24h2 + 10h – 6 = 2(4h + 3)(3h – 1) Include the GCF in your final answer.
7-7

9. Factoring Special Cases
ALGEBRA 1 LESSON 7-7
Factor each expression.
1. y2 – 18y a2 – 24a + 16
3. p2 – x2 – 225
5. 5m2 – c2 + 20c + 50
(y – 9)2
(3a – 4)2
(p + 13)(p – 13)
(6x + 15)(6x – 15)
5(m + 3)(m – 3)
2(c + 5)2
7-7

10. Factor each expression. 1. 10p3 – 25p2 + 4p – 10
Factoring by Grouping
ALGEBRA 1 LESSON 7-7
Factor each expression.
1. 10p3 – 25p2 + 4p – 10
2. 36x4 – 48x3 + 9x2 – 12x
3. 16a3 – 24a2 + 12a – 18
(5p2 + 2)(2p – 5)
3x(4x2 + 1)(3x – 4)
2(4a2 + 3)(2a – 3)
7-7