The document is a mathematics lesson on factoring polynomials using the greatest common factor and factoring techniques. It defines key terms like GCF, prime factors, monomials, binomials, and trinomials. It provides examples of finding the GCF of monomial expressions and factoring polynomials. It also lists additional factoring identities for differences and sums of cubes. The lesson aims to teach students how to rewrite polynomial expressions as products of smaller degree polynomials using factoring methods.

1. Mathematics 8
with Ma’am Mary Jhoy S. Pelayo

2. Today's Lesson
FACTORING
USING
COMMON
MONOMIAL
FACTOR

3. Unlocking Word Difficulty
1. GCF
2. Prime Factor
3. Monomial
4. Binomial
5. Trinomial
4. Polynomial
=GreatestCommonFactor
=Numbersthathaveonlyonefactor=2,3,5,7
=8y2,5x,-9ab,21a,-3a2x
=8y2+5x,-9ab+21a,-a2-4
=xy+2x-3y,x 2 +2x-3
=algebraicexpressionsthatconsistofvariables
andcoefficients.

4. GREATEST COMMON FACTOR
Refers to the common factor having the
greatest numerical factor and with
variables having the least degree.
Example 1: 6x2 and 15x4

5. 1. 6a and 18ab
2. 10a and 12𝑎2
b
3. 8𝑥2
y and 16xy
4. 8a𝑏3
and 10𝑎2
𝑏2
5. 9𝑥2
and 6xy
Find the GCF of each pair of monomials.

6. 6. 8𝑥2
and 12x
7. 3𝑤3
and 6𝑤2
8. 15𝑥2
and 21𝑦2
Find the GCF of each pair of monomials.

7. FACTORING POLYNOMIAL
-rewriting a polynomial as a
product of polynomials of
smaller degree.

8. FACTORING POLYNOMIAL
Example 1: 4𝑥2
+ 6x
Example 2: 3𝑥2
+ 6
Example 3: 8𝑥2
+ 12x
Example 4: 6𝑥4
– 14𝑥2

9. Quiz 1
Factor each expression.
1. 4x + 2y
2. 10b + 5c
3. 16𝑥2
– 12x
4. 15x𝑦2
+ 25xy
5. 2𝑦2
+ 20y

10. Other Examples
Factor each expression.
1. 6a + 8𝑎2
b - 14𝑎3
𝑏2
2. 18𝑥5
𝑦 + 12𝑥4
𝑦 − 3𝑥2
𝑦
3. 10 𝑥3
+ 9𝑥2
+ 4𝑥
4. 8𝑥2
+ 2xy + 4𝑥𝑦2
5. 3𝑥3
𝑦3
+ 5𝑥2
𝑦2
+ 2𝑥𝑦5

11. ADDITIONAL INFORMATION
a2 − b2 = (a+b)(a−b)
a2 + 2ab + b2 = (a+b)(a+b)
a2 − 2ab + b2 = (a−b)(a−b)
a3 + b3 = (a+b)(a2−ab+b2)
a3 − b3 = (a−b)(a2+ab+b2)
a3+3a2b+3ab2+b3 = (a+b)3
a3−3a2b+3ab2−b3 = (a−b)3