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1. Grade 8 – Mathematics
Quarter I
FACTORING QUADRATIC TRINOMIALS
of the form 𝒙 𝟐
+ 𝒃𝒙 + 𝒄

2. Objectives:
1. factor quadratic trinomials of the
form 𝑥2
+ 𝑏𝑥 + 𝑐 ; and
2. solve problems involving factors
of polynomials.

3. List all pairs of integers (factors) of the
following numbers.
4
1 and 4
2 and 2
10
1 and 10
2 and 5
8
1 and 8
2 and 4
6
1 and 6
2 and 3

4. List all pairs of integers (factors) of the
following numbers.
12
1 and 12
2 and 6
3 and 4
30
1 and 30
2 and 15
3 and 10
20
1 and 20
2 and 10
4 and 5
18
1 and 18
2 and 9
3 and 6

5. FACTORING.
𝒙 𝟐
+ 𝒃𝒙 + 𝒄
1. List all pairs of integers (m · n) whose
product is c.
2. Choose a pair whose sum (m + n) is b.
𝒙 𝟐
+ 𝒃𝒙 + 𝒄 = (x + m)(x + n)

6. FACTORING.
𝒙 𝟐
+ 𝒃𝒙 + 𝒄
𝒙 𝟐
+ 𝒃𝒙 + 𝒄 = (x + m)(x + n)
(m · n)(m + n)
Factored Form

7. Example: 𝒙 𝟐
+ 𝟏𝟎𝒙 + 𝟏𝟔
List all pairs of integers whose product is c.
1 and 16 2 and 8 4 and 4
Choose a pair whose sum is b.
2 and 8 = 10
Factor as (x + m)(x + n).
m n
𝒙 𝟐
+ 𝟏𝟎𝒙 + 𝟏𝟔 = (x + 2)(x + 8)
(+)(+)
(-)(-)

8. Example: 𝒙 𝟐
− 𝟗𝒙 + 𝟏𝟖
List all pairs of integers whose product is c.
-1 and -18 -2 and -9 -3 and -6
Choose a pair whose sum is b.
-3 and -6 = -9
Factor as (x + m)(x + n).
m n
𝒙 𝟐
− 𝟗𝒙 + 𝟏𝟖 = (x - 3)(x - 6)
(+)(+)
(-)(-)

9. Example: 𝒙 𝟐
− 𝟐𝒙 − 𝟐𝟒
List all pairs of integers whose product is c.
1 and -24 2 and -12 4 and -6 3 and -8
Choose a pair whose sum is b.
4 and -6 = -2
Factor as (x + m)(x + n).
m n
𝒙 𝟐
− 𝟐𝒙 − 𝟐𝟒 = (x + 4)(x - 6)
(+) (-)larger
integer

10. Example: 𝒙 𝟐
+ 𝟑𝒙 − 𝟏𝟎
List all pairs of integers whose product is c.
-1 and 10 -2 and 5
Choose a pair whose sum is b.
-2 and 5 = 3
Factor as (x + m)(x + n).
m n
𝒙 𝟐
+ 𝟑𝒙 − 𝟏𝟎 = (x - 2)(x + 5)
(+) (-)larger
integer

11. Example: 𝒙 𝟐
+ 𝟑𝒙 + 𝟑
List all pairs of integers whose product is c.
1 and 3
since 1 and 3 = 4
PRIME TRINOMIAL
then 𝒙 𝟐
+ 𝟑𝒙 + 𝟑 cannot be factored
using integer coefficients, then it is…
(+)(+)
(-)(-)

12. Example:
Use factoring to find the dimensions of the
given box with volume represented by the
expression 𝟒𝒙 𝟑
+ 𝟏𝟔𝒙 𝟐
− 𝟒𝟖𝒙
The dimension of the box are
4x, x + 6 and x – 2
𝟒𝒙(𝒙 𝟐
+ 𝟒𝒙 − 𝟏𝟐)Factor out 4x.
4x(x + 6)(x – 2)Factor (𝒙 𝟐
+𝟒𝒙 − 𝟏𝟐)

13. Summary.
𝒙 𝟐
+ 𝟕𝒙 + 𝟏𝟎 (+)(+) or (-)(-)
𝒙 𝟐
− 𝟕𝒙 + 𝟏𝟎 (+)(+) or (-)(-)
𝒙 𝟐
+ 𝟑𝒙 − 𝟏𝟎 (+) (-)
𝒙 𝟐
− 𝟑𝒙 − 𝟏𝟎
larger integer
(+) (-)
larger integer