1. Lesson Objective: I will be able to …
Factor quadratic trinomials of the form
ax2 + bx + c
Language Objective: I will be able to …
Read, write, and listen about vocabulary, key
concepts, and examples

2. Page 15

3. Example 1: Factoring ax2 + bx + c by Box and Diamond
Page 16
Factor 6x2 + 11x + 4 by box and diamond.
6x2 + 11x + 4
6x2 ● 4 = 24x2
24x2 1 3x 4 3x 8x 2x
6x2 8x
11x 3x 4
Use the Generic Rectangle to factor the trinomial.
Step 1 Factor out the GCF from first column.
Step 2 3x ● ? = 6x2
Step 3 2x ● ? = 8x
Step 4 4 ● ? = 4
6x2 + 11x + 4 = (2x + 1)(3x + 4)

4. To factor a2 + bx + c, check the factors of a and the factors of c in the binomials. The sum of the products of the outer and inner terms should be b.
Product = a
Product = c
Sum of outer and inner products = b
( X + )( x + ) = ax2 + bx + c

5. Example 2: Factoring ax2 + bx + c by Guess and Check
Page 17
Factor 3x2 – 16x Check your answer.
a = 3 and c = 16,
Outer + Inner = –16.
( x + )( x + )
Factors of 3 Factors of 16 Outer + Inner 
1 and 3
–1 and –16
1(–16) + 3(–1) = –19 
1 and 3
– 2 and – 8
1( – 8) + 3(–2) = –14 
1 and 3
– 4 and – 4
1( – 4) + 3(– 4)= –16
(x – 4)(3x – 4)
Use the Foil method.
Check (x – 4)(3x – 4) = 3x2 – 4x – 12x + 16
= 3x2 – 16x + 16 

6. Example 3: Factoring ax2 + bx + c with Negatives
Page 18
Factor 3n2 + 11n – 4 . Check your answer.
3n2 + 11n – 4
3n2 ● -4 = -12n2
-12n2 4
12n -4
12n -n n
3n2 -n
11n 3n -1
Use the Generic Rectangle to factor the trinomial.
Step 1 Factor out the GCF from first column.
Step 2 3n ● ? = 3n2
Step 3 n ● ? = -n
Step ● ? = -4
3x2 + 11x – 4 = (n + 4)(3n – 1)

7. When the leading coefficient is negative, factor out –1 from each term before using other factoring methods.
When you factor out –1 in an early step, you must carry it through the rest of the steps.
Caution

8. Example 4: Factoring ax2 + bx + c When a is Negative
Page 19
Factor –2x2 – 5x – 3.
–1(2x2 + 5x + 3)
Factor out –1.
a = 2 and c = 3;
Outer + Inner = 5
–1( x + )( x+ )
Factors of 2 Factors of Outer + Inner 
1 and 2
3 and 1
1(1) + 3(2) = 7 
1 and 2
1 and 3
1(3) + 1(2) = 5
(x + 1)(2x + 3)
–1(x + 1)(2x + 3), or
–(x + 1)(2x + 3)

9. Chapter 8 Quick Review Assignment #14
1. Write the prime factorization of 48.
2. Factor out the GCF: 18x2y4 – 27xy3
3. Factor: x2 – 6x + 8
4. Factor: 3n2 + 16n + 21

10. Classwork
Chapter 8 Quiz

11. Homework
Assignment #14
Holt 8-4 #36, 39, 42, 45, 48, 51, 54, 67, 68, 70, 77 – 82
Holt 8-3 #33 – 36, 38 – 43
KIN 8-5