1. To factor non-perfect square trinomials, determine the factors of the leading term and the factors of the constant term that can be combined to form the middle term. 2. Trinomials of the form x^2 + bx + c can be factored into the product of two binomials by finding factor pairs of the constant term c that have a sum of b. 3. Examples are provided of factoring trinomials of the form a^2 + 10a + 25, m^2 + 10m + 21, and b^2 + 14b + 45.

1. Factoring Non-
Perfect Square
Trinomials

2. In factoring Non-Perfect Square
Trinomial, consider to determine
the factors of the leading (square)
term; the factors of the last
(constant) term may be combined
to find the coefficient of the
middle term.

3. Trinomials of the form 𝒙 𝟐 + bx + c
are the products of two binomials.
Observe how the last term and the
middle term of the resulting
trinomial are generated.

4. ( x + ___ ) ( x + ___ )
Factor Pairs of 6
1 x 6
2 x 3
Corresponding sum
1 + 6 = 7
2 + 3 = 5
𝒙 𝟐 + 5x + 6 = ( x + 2 ) ( x + 3 )

5. 𝟐. 𝑭𝒂𝒄𝒕𝒐𝒓 𝒂 𝟐
+ 10a + 25
Factor Pairs of 25
1 x 25
5 x 5
Corresponding sum
1 + 25 = 26
5 + 5 = 10
𝒂 𝟐
+ 10a + 25 = 𝑎 + 5 (𝑎 + 5 )

6. 𝟑. 𝑭𝒂𝒄𝒕𝒐𝒓 𝒎 𝟐
+ 10m + 21
Factor Pairs of 21
1 x 21
7 x 3
Corresponding sum
1 + 21 = 22
7+ 3 = 10
𝒎 𝟐
+ 10m + 21 = 𝑚 + 7 (𝑚 + 3)
𝑚 + 3 (𝑚 + 7)
𝑜𝑟

7. 𝟒. 𝑭𝒂𝒄𝒕𝒐𝒓 𝒃 𝟐
+ 14b + 45
Factor Pairs of 21 Corresponding sum
𝒃 𝟐
+ 14b + 45 = 𝑏 + 9 (𝑚 + 5)

8. 𝟓. 𝑭𝒂𝒄𝒕𝒐𝒓 𝒔 𝟐
+ 2s - 15
Factor Pairs of -15
5 x -3
-5 x 3
Corresponding sum
1 + -15 =
-1 + 15 =
𝒔 𝟐
+ 2s -15 = 𝑠 + 5 (𝑠 − 3)
𝑠 − 3 (𝑠 + 5)
𝑜𝑟
1 x -15
-1 x 15
-14
14
5 + -3 = 2
-5 + 3 = -2

10. 7. Factor 𝒔 𝟐
- 4s - 45
Factor Pairs of -45
1 x - 45
-1 x 45
5 x - 9
-5 x 9
3 x - 15
-3 x 15
Corresponding sum
1 + - 45 = - 44
-1 + 45 = 44
5 + -9 = -4
-5 + 9 = 4
3 + - 15 = -12
-3 + 15 = 12
𝒔 𝟐 - 4s – 45 = (𝒔 + 5 ) (𝒔 - 9 ) 𝒐𝒓
𝒔 − 𝟗 (𝒔 + 𝟓 )

11. 7. Factor 𝒛 𝟐
+ 5z - 24
Factor Pairs of -45
1 x - 24
-1 x 24
4 x - 6
-4 x 6
3 x - 8
-3 x 8
Corresponding sum
1 + - 24 = - 23
-1 + 24 = 23
4 + -6 = -2
-4 + 6 = 2
3 + - 8 = -5
-3 + 8 = 5
𝒛 𝟐 + 5z – 24 = (𝒛 - 3 ) (𝒛 + 8 ) 𝒐𝒓
𝒛 + 𝟖 (𝒛 − 𝟑 )