FACTORING BY GREATEST COMMON MONOMIAL FACTOR

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At the end of the lesson, the students will be able to;

1. Define Common Monomial Factoring

2. Identify factors of a given expression of a monomial; and

3. Factor polynomials using Common Monomial Factor.

Factor – number on algebraic expression that divides another number evenly with no remainder.

Greatest Common Factor – is the largest number that is a factor of two or more numbers.

​width(w)

​length(l)

​in order for us to find the area of this rectangle, we will use the formula;

area= length x width

​Let's see this rectangle;

​w= 2 units

​l= (x+3) units

area= l x w
area= (x+3) x 2
area= 2x+6 square units

For example;

​let l= (x+3) and w= 2

therefore, the area of this rectangle is 2x+6 sq. units

​To find the GCMF of each pair of monomials, we will use the following steps:

Step 1: Factor each monomial.

Step 2: Identify the common factors.

Step 3: Find the product of the common factors.

​Example 1. Find the GCMF of each pair of monomials.
a.  (4x)³ and (8x)²

​Example 1. Find the GCMF of each pair of monomials.
a.  (4x)³ and (8x)²

Step 1: Factor each monomial.
4x³= 2⋅2⋅x⋅x⋅x
8x²= 2⋅2⋅2⋅x⋅x

​Example 1. Find the GCMF of each pair of monomials.
a.  (4x)³ and (8x)²

Step 1: Factor each monomial.
4x³= 2⋅2⋅x⋅x⋅x
8x²= 2⋅2⋅2⋅x⋅x

Step 2: Identify the common factors.
2⋅2⋅x⋅x

​Example 1. Find the GCMF of each pair of monomials.
a.  (4x)³ and (8x)²

Step 1: Factor each monomial.
4x³= 2⋅2⋅x⋅x⋅x
8x²= 2⋅2⋅2⋅x⋅x

Step 2: Identify the common factors.
2⋅2⋅x⋅x

Step 3: Find the product of the common factors.
2⋅2⋅x⋅x= 4x²

​Example 1. Find the GCMF of each pair of monomials.
b.  15y⁶ and 9z

Step 1: Factor each monomial.
15y⁶= 3⋅5⋅y⋅y⋅y⋅y⋅y⋅y
9z= 3⋅3⋅z

Step 2: Identify the common factors.
3

Step 3: Find the product of the common factors.
3

​Step 1. Determine the number of terms.

Step 2. Determine the GCF of the Numerical Coefficients. Determine the GCF of the variables.

Step 3. Find the product of GCF of the numerical coefficient and variables.

Step 4. Find the other factor by dividing each term of polynomial by the GCF.

Step 5. Write the complete factored form.

​Step 1. Determine the number of terms.
6x and 3x²

​Step 1. Determine the number of terms.
6x and 3x²

Step 2. Determine the GCF of the Numerical Coefficients. Determine the GCF of the variables.
3⋅2⋅x
3⋅x⋅x

​Step 1. Determine the number of terms.
6x and 3x²

Step 2. Determine the GCF of the Numerical Coefficients. Determine the GCF of the variables.
3⋅2⋅x
3⋅x⋅x

Step 3. Find the product of GCF of the numerical coefficient and variables.
=3x

​Step 1. Determine the number of terms.
6x and 3x²

Step 2. Determine the GCF of the Numerical Coefficients. Determine the GCF of the variables.
3⋅2⋅x
3⋅x⋅x

Step 3. Find the product of GCF of the numerical coefficient and variables.
=3x

Step 4. Find the other factor by dividing each term of polynomial by the GCF.
6x/3x + 3x²/3x= 2+x

​Step 1. Determine the number of terms.
6x and 3x²

Step 2. Determine the GCF of the Numerical Coefficients. Determine the GCF of the variables.
3⋅2⋅x
3⋅x⋅x

Step 3. Find the product of GCF of the numerical coefficient and variables.
=3x

Step 4. Find the other factor by dividing each term of polynomial by the GCF.
6x/3x + 3x²/3x= 2+x

Step 5. Write the complete factored form.
=3x(2+x)

​Example 2: 12x³-18xy+24x  

​Step 1. Determine the number of terms.
12x³, 18xy and 24x  

Step 2. Determine the GCF of the Numerical Coefficients. Determine the GCF of the variables.
6⋅2⋅x⋅x⋅x
6⋅3⋅x⋅y
6⋅4⋅x

Step 3. Find the product of GCF of the numerical coefficient and variables.
=6x

Step 4. Find the other factor by dividing each term of polynomial by the GCF.
12x³/6x-18xy/6x+24x/6x= 2x²-3y+4

Step 5. Write the complete factored form.
=6x(2x²-3y+4)

​Example 3: 12x³y⁵-20x⁵y²z

​Step 1. Determine the number of terms.
 12x³y⁵ and 20x⁵y²z

Step 2. Determine the GCF of the Numerical Coefficients. Determine the GCF of the variables.
4⋅3⋅x⋅x⋅x⋅y⋅y⋅y⋅y⋅y
4⋅5⋅x⋅x⋅x⋅x⋅x⋅y⋅y⋅z
Step 3. Find the product of GCF of the numerical coefficient and variables.

= 4x³y²

Step 4. Find the other factor by dividing each term of polynomial by the GCF.
12x³y⁵/4x³y² -20x⁵y²z/4x³y²= 3y³-5x²z

Step 5. Write the complete factored form.
= 4x³y²(3y³-5x²z)