Competency 1.1 based on DepEd MELC

1. Prepared by: Gauben L. Malicsi
Factoring Out the Greatest Common Factor (GCF)
A natural number larger than 1 that has no factors other than itself
and 1 is called prime number. The numbers, 2, 3, 5, 7, 11, 13, 17, 19, 23
are the first nine prime numbers. There are infinitely many prime numbers.
To factor a natural numbers completely means to write it as a product
of prime numbers. In factoring 12, we might write 12 = 4 x 3. However, 12
is not factored completely as 4 x 3 because 4 is not a prime. To factor
completely, we write 12 = 2 x 2 x 3.
The greatest common factor (GCF) is a monomial that includes every
number or variable that is a factor of all terms of the polynomial.
We can use the following strategy for finding the greatest common
factor of a group of terms.
Strategy for Finding the Greatest Common Factor (GCF)
1. Find the greatest common factor of the numerical coefficients.
2. Find the variable with the least exponent that appears in each term of
the polynomial.
3. The product of the greatest common factor in (a) and (b) is the GCF of
the polynomial.
4. To completely factor the given polynomial, divide the polynomial by
its GCF, the resulting quotient is the other factor.
EXAMPLE 1: Factoring out the greatest common factor
Factor each polynomial by factoring out the GCF.
a. 5𝑥4
− 10𝑥3
+ 15𝑥2
b. 8𝑥𝑦2
+ 20𝑥2
𝑦
SOLUTIONS:
a. 5𝑥4
− 10𝑥3
+ 15𝑥2
 Find the GCF of the numerical coefficients.
5 = 5 x 1 10 = 5 x 2 15 = 5 x 3
The common factor is 5. So, the GCF for numerical coefficients is 5.
 Find the variable with the least exponent that appears in each term
of the polynomial.
𝑥4
𝑥3
𝑥2
The least exponent for x is 2. Therefore, the GCF for variable is 𝑥2
 Find the product of (a) and (b).
(5)(𝑥2
) = 5𝑥2
5𝑥2
is now the GCF of the polynomial
 Divide the polynomial by its GCF, the resulting quotient is the other
factor.
5𝑥4
− 10𝑥3
+ 15𝑥2
= 5𝑥2
(𝑥2
− 2𝑥 + 3)
b. 8𝑥𝑦2
+ 20𝑥2
𝑦
 Find the greatest common factor of the numerical coefficients.
8 = 4 x 2 20 = 4 x 5
The common factor is 4. So, the GCF for numerical coefficients is 4.
 Find the variable with the least exponent that appears in each term
of the polynomial.
𝑥𝑦2
𝑥2
𝑦
Factoring polynomials with
common monomial factor
Factors
completely
polynomials with
common monomial
factor
COMPETENCY 1.1

2. Prepared by: Gauben L. Malicsi
The least exponent for both x and y is 1. Therefore, the GCF for variables
is 𝑥𝑦.
 Find the product of (a) and (b).
(4)(xy) = 4xy
4xy is now the GCF of the polynomial
 Divide the polynomial by its GCF, the resulting quotient is the other
factor.
8𝑥𝑦2
+ 20𝑥2
𝑦 = 4𝑥𝑦(2𝑦 + 5𝑥)
EXAMPLE 2: Factoring out binomial
Factor.
a. (x + 3)w + (x + 3)a b. x(x – 9) – 4(x – 9)
SOLUTIONS:
a. We treat x + 3 like a common monomial when factoring:
(x + 3)w + (x + 3)a = (x + 3)(w + a)
b. Factor out the common binomial x – 9:
x(x – 9) – 4(x – 9) = (x – 4)(x – 9)
PERFORMANCE TASK
Direction: Complete the table below.
Polynomial Greatest Common
Monomial Factor
(CMF)
Quotient of
Polynomial and
CMF
Factored Form
6m + 8 2 3m + 4 2(3m+4)
4𝑚𝑛2
4𝑚𝑛2
(3𝑚 + 𝑛)
18𝑑2
𝑜3
𝑡6
− 15𝑑6
𝑜4
6𝑡6
− 5𝑑4
4(12) + 4(8) 4
12𝑤𝑖3
𝑛5
− 16𝑤𝑖𝑛
+ 20𝑤𝑖𝑛𝑛𝑒𝑟
ASSESSMENT TASK
Show your solutions on the box provided below and write your final answer
on the space before the number.
1. Factor out the greatest common factor in each expression. (See Example
1)
a. 𝑥3
− 5𝑥
b. 10𝑥2
− 20𝑦3
c. 42𝑤𝑧 + 28𝑤𝑎
2. Factor out the greatest common factor in each expression. (See Example
2)
a. (x – 6)a + (x – 6)b
b. w – 2)y +(w – 2)3
YOUR SOLUTIONS:
1. 2. 3.
4. 5.

3. Prepared by: Gauben L. Malicsi
INDICATORS Meets
Standard of
Excellence
Approaching
Standard of
Excellence
Meets
Acceptable
Standard
Does Not Meet
Acceptable
Standard
CRITERIA 4 3 2 1
Performance
Task
Shows
exemplary
performance
Demonstrates
solid
performance
and
understanding
With some
errors and
mastery is
not thorough.
Has errors,
omission and
misconception.
Assessment
Task
With 5
correct
answers
With 4
correct
answers
With 3
correct
answers
With less than
3 correct
answers
Completeness Has all
aspects of
work that
exceed level
of
expectation
Has some
aspects of
work that
exceed level
of
expectation
Has minimal
aspects of
work that
meet level of
expectation
No aspect of
work meets
level of
expectations
Neatness The learning
tasks are
done very
neatly.
The learning
tasks are
done neatly.
The learning
tasks are
done quite
neatly.
The learning
tasks are
poorly done
and need
improvement.
Submission of
Requirements
The assigned
learning
tasks are
submitted on
or before the
deadline.
The assigned
learning
tasks are
submitted a
day after the
deadline.
The assigned
learning
tasks are
submitted two
days after
the deadline.
The assigned
learning tasks
are submitted
three days
after the
deadline.
TOTAL SCORE
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