1. 7-3 Factoring x2 + bx + c Warm Up Lesson Presentation Cornell Notes
Lesson Quiz
Holt McDougal Algebra 1
Holt Algebra 1

2. Warm Up /25/17
1. Which pair of factors of 8 has a sum of 9?
2. Which pair of factors of 30 has a sum of –17?
Multiply.
3. (x +2)(x +3)

3. Essential Questions
1. How do you factor quadratic trinomials of the form x2 + bx + c?

4. (x + 2)(x + 5) = x2 + 7x + 10

5.    Example Factor x2 + 15x + 36 by guess and check.
Steps: 1. Write two sets of parentheses.
2. Split up the first term x2.
3. Factors of 36 are: 
(x + 1)(x + 36) = x2 + 37x + 36 
(x + 2)(x + 18) = x2 + 20x + 36 
(x + 3)(x + 12) = x2 + 15x + 36
The factors of x2 + 15x + 36 are (x + 3)(x + 12).

6.     Example Factor each trinomial by guess and check.
x2 + 10x + 24
Steps: 1. Write two sets of parentheses.
2. Split up the first term x2.
3. Factors of 24 are: 
(x + 1)(x + 24) = x2 + 25x + 24 
(x + 2)(x + 12) = x2 + 14x + 24 
(x + 3)(x + 8) = x2 + 11x + 24 
(x + 4)(x + 6) = x2 + 10x + 24
The factors of x2 + 10x + 24 are (x + 4)(x + 6).

7.    I do…. Factor each trinomial by guess and check. x2 + 7x + 12
Steps: 1. Write two sets of parentheses.
2. Split up the first term x2.
3. The factors of 12 are: 
(x + 1)(x + 12) = x2 + 13x + 12
Try factors of 12 for the constant terms in the binomials. 
(x + 2)(x + 6) = x2 + 8x + 12 
(x + 3)(x + 4) = x2 + 7x + 12
The factors of x2 + 7x + 12 are (x + 3)(x + 4).

8. x2 12
(x + 3)(x +4) = x2 + 7x + 12 3x 4x

9. We do! Factoring x2 + bx + c When c is Positive
Factor each trinomial. Check your answer.
x2 + 6x + 9
(x + __)(x + __)
Factors of 9 Sum
1 and 
3 and 
The factors needed are 3 and 3.
(x + 3)(x + 3)
Check (x + 3)(x + 3 ) = x2 +3x + 3x + 9
= x2 + 6x + 9 

10. You do! Factoring x2 + bx + c When c is Positive
Factor each trinomial. Check your answer.
x2 – 8x + 15
(x + __)(x + __)
Factors of 15 Sum
–1 and –15 –16 
–3 and –5 –8 
The factors needed are –3 and –5 .
(x – 3)(x – 5)
Check (x – 3)(x – 5 ) = x2 – 3x – 5x + 15
= x2 – 8x + 15 

11.    Example: Factoring x2 - bx + c: When b is Negative
x2 – 13x + 40 =
(x + __)(x+ __)
Factors of 40 Sum 
–2 and –20 –22
–4 and –10 –14 
–5 and – –13
(x – 5)(x – 8)
Check (x – 5)(x – 8) = x2 – 5x – 8x + 40
= x2 – 13x + 40 

12.   Example: Factoring x2 + bx - c When c is Negative (x + __)(x + __)
Factors of –20 Sum 
–1 and
–2 and 
–4 and
(x – 4)(x + 5)

13.   Example: Factoring x2 - bx - c When b & c are Negative
x2 – 3x – 18 =
(x + __)(x + __)
Factors of –18 Sum 
1 and – –17
2 and – – 7 
3 and – – 3
(x – 6)(x + 3)

14. Lesson Quiz: Part I
Factor each trinomial.
1. x2 – 11x + 30
2. x2 + 10x + 9
3. x2 – 6x – 27
4. x2 + 14x – 32