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1. TO OUR CLASS
MATHEMATICS 8

2. Lesson 1: Factoring Polynomials
At the end of the lesson, you should be able to:
• factor completely different types of polynomials (polynomials
with common monomial factor, difference of two squares, sum
and difference of two cubes, perfect square trinomials, and
general trinomials) (M8AL-Ia-b-1); and
• solve problems involving factors of polynomials (M8AL-Ib-2).
What to expect?

3. Review Find the Greatest Common
Factor of the following:
2.) 15, 20 & 25
Answer: 5
1.) 36 & 42
Answer: 6
3.) 4, 8 & 16
Answer: 4
4.) 18 & 36
Answer: 18
5. 6, 15, 21 & 27
Answer: 3

4. Factoring Polynomials with a Common Factor
Examples: Factor the following expressions.
1. 2𝑥3
+ 3𝑥5
2. 12𝑥3
𝑦4
− 24𝑥𝑦3
+ 16𝑥4
𝑦9
3. 3𝑥 − 12
4. 𝑥2
𝑦2
− 3𝑥𝑦2
Product Form Factored Form
2 + 3𝑥2
(3𝑥2
𝑦 − 6 + 4𝑥3
𝑦6
)
𝑥 − 4
(𝑥 − 3)
𝑥3
4𝑥𝑦3
3
𝑥𝑦2

5. Perfect Square Trinomials
Form of Special Product Form of its Factor(s)
1. 4𝑥2
+ 12𝑥 + 9
Examples:
1st term – 2x
Last term – 3
2. 25𝑥4
− 20𝑥2
+ 4
1st term – 5𝑥2
Last term – 2
= (2𝑥 + 3)2 = (5𝑥2 − 2)2
3. 4𝑥2
− 20𝑥𝑦 + 25𝑦2
1st term – 2x
Last term – 5y
= (2𝑥 − 5𝑦)2
𝑎2
+ 2𝑎𝑏 + 𝑏2
𝑎2
− 2𝑎𝑏 + 𝑏2
𝑎 + 𝑏 𝑎 + 𝑏 = (𝑎 + 𝑏)2
𝑎 − 𝑏 𝑎 − 𝑏 = (𝑎 − 𝑏)2

6. Factor the following expressions.
1. 𝑦3
+ 9𝑦2
2. 5𝑥2
𝑦3
+ 15𝑥3
𝑦2
3. 𝑥2
+ 10𝑥 + 25
4. 𝑥2
−10𝑥 + 25
5. 4𝑦2
− 32𝑦 + 64
𝑦2
(𝑦 + 9)
5𝑥2
𝑦2
(𝑦 + 3𝑥)
(𝑥 + 5)(𝑥 + 5)
(𝑥 − 5)(𝑥 − 5)
(2𝑦 − 8)(2𝑦 − 8)