1. The document discusses factoring general trinomials of the form ax^2 + bx + c where a = 1. It provides examples of factoring various trinomial expressions. 2. Students are asked to factor trinomials and check their understanding of the factoring process. Several exercises and activities are provided to help students practice factoring trinomials. 3. The objective is for students to learn how to factor general trinomials of the form ax^2 + bx + c where a = 1.

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L.C. M8AL-Ia-b-1: Factor general trinomials of the form ax2 + bx G r a d e 8
G R A D E 8
M A T H E M A T I C S
FACTORING

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L.C. M8AL-Ia-b-1: Factor general trinomials of the form ax2 + bx G r a d e 8
Content Standard:
The learner demonstrates understanding of key
concepts of factors of polynomials.
Performance Standard:
The learner is able to formulate real-life problems
involving factors of polynomials and solves these with
utmost accuracy using a variety of strategies.

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L.C. M8AL-Ia-b-1: Factor general trinomials of the form ax2 + bx G r a d e 8
Objective:
At the end of the lesson, the students should be able to:
1. factor general trinomial ax2 + bx + c = 0 where a = 1.

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L.C. M8AL-Ia-b-1: Factor general trinomials of the form ax2 + bx G r a d e 8
Give two numbers that satisfy the given conditions.
1. Product = 12, sum = 8.
2. Product = 35, sum = 12.
3. Product = 24, sum = 11.
4. Product = 48, sum = -14.
5. Product = -60, sum = -11.
Are You Ready???

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L.C. M8AL-Ia-b-1: Factor general trinomials of the form ax2 + bx G r a d e 8
Think of this!
If the area of a rectangular field is (x2 + 5x + 6)m2 , what are its
dimensions?
(x2 + 5x + 6)m2

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L.C. M8AL-Ia-b-1: Factor general trinomials of the form ax2 + bx G r a d e 8
Activity 1:

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L.C. M8AL-Ia-b-1: Factor general trinomials of the form ax2 + bx G r a d e 8

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L.C. M8AL-Ia-b-1: Factor general trinomials of the form ax2 + bx G r a d e 8
Answer the following:
1. What is the total area of each figure?
2. Using the sides of the tiles, write all the dimensions of the
rectangles.
3. How did you get the dimensions of the rectangles?
4. Did you find difficulty in getting the dimensions?

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L.C. M8AL-Ia-b-1: Factor general trinomials of the form ax2 + bx G r a d e 8
Activity 2: Observe then answer the given question.
1. Factor x2 + 5x + 6
Solution: b = 5, c = 6
𝑥2
+ 5𝑥 + 6 = (𝑥 + ______)(𝑥 + ______)
Factors of c = 6 Sum of factors
1, 6 1 + 6 = 7
2, 3 2 + 3 = 5
-1, -6 -1 + (-6) = -7
-2, -3 -2 + (-3) = -5

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L.C. M8AL-Ia-b-1: Factor general trinomials of the form ax2 + bx G r a d e 8
2. Factor m2 + 4m -21.
𝑚2 + 4𝑚 − 21 = ( )( )
Factors of -21 Sum of factors

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L.C. M8AL-Ia-b-1: Factor general trinomials of the form ax2 + bx G r a d e 8
2. Factor 2q3 – 6q2 - 36q.
2𝑞3 − 6𝑞2 − 36𝑞 = _______( )( )
Factors Sum of factors

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L.C. M8AL-Ia-b-1: Factor general trinomials of the form ax2 + bx G r a d e 8
Let’s Do It!!!
A. Factor the following:
1. 𝑥2
+ 11𝑥 + 28
2. 𝑧2
− 10𝑧
+ 9
3. 𝑏2
− 𝑏 − 42
4. 𝑦2
− 14𝑦 + 45
5. 3𝑤3
+ 9𝑤2
− 84𝑤

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L.C. M8AL-Ia-b-1: Factor general trinomials of the form ax2 + bx G r a d e 8
Let’s wrap up…
How do you factor general trinomials of the form ax2 + bx + c
whose a = 1?

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L.C. M8AL-Ia-b-1: Factor general trinomials of the form ax2 + bx G r a d e 8
Do this!!!
Factor the following:
1. 𝑥2
+ 2𝑥𝑦 − 35𝑦2
2. 𝑎2
− 2𝑎𝑏 − 99𝑏2
3. 𝑐2
− 𝑐𝑑 − 56𝑑2
4. y2
+ 6yz − 72z2
5. 2𝑘3
− 2𝑘2
− 40𝑘

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L.C. M8AL-Ia-b-1: Factor general trinomials of the form ax2 + bx G r a d e 8
Do It More!!!
Bingo Factor Game

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L.C. M8AL-Ia-b-1: Factor general trinomials of the form ax2 + bx G r a d e 8
HAPPY TO LEARN!!!
I MATH!!!

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L.C. M8AL-Ia-b-1: Factor general trinomials of the form ax2 + bx G r a d e 8
Reference:
Grade 8 Teaching Guide, p. 41-43

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L.C. M8AL-Ia-b-1: Factor general trinomials of the form ax2 + bx G r a d e 8

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L.C. M8AL-Ia-b-1: Factor general trinomials of the form ax2 + bx G r a d e 8
Key Answer to Let’s Do It:
1. 𝑥2 + 11𝑥 + 28 = (x + 7)(x + 4)
2. 𝑧2
−10𝑧
+ 9= (z − 9)(z − 1)
3. 𝑏2 − 𝑏 − 42 = (b + 6)(b - 7)
4. 𝑦2−14𝑦 + 45 = (y − 9)(y − 5)
5. 3𝑤3+ 9𝑤2 − 84𝑤 = 3w (w + 7)(w − 4)

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L.C. M8AL-Ia-b-1: Factor general trinomials of the form ax2 + bx G r a d e 8
Key Answer to Do This:
Factor the following:
1. 𝑥2 + 2𝑥𝑦 − 35𝑦2 = (x + 7y) (x – 5y)
2. a2
− 2ab − 99b2
= (a + 9b) (a – 11b)
3. 𝑐2 − 𝑐𝑑 − 56𝑑2 = (c + 7d) (c – 8d)
4. y2 + 6yz − 72z2 = (y + 12z) (y – 6z)
5. 2𝑘3 − 2𝑘2 − 40𝑘 = 2k(k + 4) (k - 5)