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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)
Editor's Notes
Guide Questions:
What is the area of square ABDC?
What is the area of the cut-out square GFDE?
What is the area of the new figure formed?
What are the length and the width of the new figure formed?
What pattern can you create in the activity?
Guide Questions:
What pair of factors gives a sum equal to the middle term?
Check your answer by multiplying the two binomials using the FOIL method.
Guide Questions:
List all the factors of -21.
Find a pair of factors of -21 whose sum is 4.
Guide Questions:
Is there a common monomial factor of the given polynomial? If yes, factor out.
Find pair of factors of -18 whose sum is -3.
On a clean sheet of paper, draw a 3x3 grid square and mark the center as FACTOR. Pick 8 different factors from the given table and write them in the grid. As I read the trinomial, you will locate its factors and mark it x. the first one who makes the x pattern wins.
(Pls. see the teaching guide, p. 43 for the polynomials.)
