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Factors of Polynomials
COMMON MONOMIAL
FACTOR
Jessebel G. Bautista
Antonio J. Villegas Voc’l High School
My
Profile
Objectives:
–recall GCF
–factor polynomials whose terms have
common monomial factor
–think deductively using ECM
–relate factoring in real life
Drill:
Give the greatest common factor (CGF) of the following
expressions.
1. 12, 15, 18
2. 24, 36, 72
3. x3, x2, x
4. x2y2, xy4, x2y2
5. 5a3, 10a2, 15a
6. 30b4, 45b2, 60b3
7. 24x2y2, 40x2y3, 48xy4
8. 100m6n8,125m3n5, 250mn
9. (x -2y)4, (x - 2y)2, (x - 2y)
10. 12(a + b)5, 36(a + b)3, 48(a + b)
Activity 1 FINDING COMMON
Description: Your task in this activity is to identify common things that are
present in the three pictures.
Questions:
1. What are the things common to these pictures?
2. Are there things that make them different?
3. Can you spot things that are found on one picture but not on the other
two?
4. What are the things common to two pictures but not on the other?
The activity in the previous slides gave
us the idea about the Greatest
Common Monomial Factor.
Now, on the next slide. Study the
example of the ECM on how factoring
the Greatest Common Monomial
Factor is being done.
Example – Conclusion Map (ECM)
Direction: Let the students write the conclusion and their example given the ECM.
Polynomial 6m + 8
GCF 2
Quotient of
Polynomial
3m + 4
Factored
Form
2 (3m +4)
Polynomial 15x2+10 xy
GCF 5x
Quotient of
polynomial
3x + 2y
Factored
Form
5x (3x +2y)
Polynomial 5t4 + 4t3 + t2
GCF t2
Quotient of
polynomial
5t2 + 4t + 1
Factored
Form
t2 (5t2 +4t + 1)
Example 1 Example 2 Example 3
Conclusion
Your own example
Examples
1. Factor : 12x3y5 – 20x5y2z
Steps 1:
Find the greatest common factor of the numerical
coefficients.
The GCF of 12 and 20 is 4.
1. Factor : 12x3y5 – 20x5y2z
Steps 2:
Find the variable with the least exponent that
appears in each term of the polynomial.
x and y are both common to all terms and 3 is
the smallest exponent for x and 2 is the
smallest exponent of y, thus, x3y2
is the GCF of the variables.
1. Factor : 12x3y5 – 20x5y2z
Steps 3:
The product of the greatest common factor in steps
(1) and (2) is the GCF of the polynomial.
4x3y2
is the GCF of 12x3y5 – 20x5y2z.
1. Factor : 12x3y5 – 20x5y2z
Steps 4:
To completely factor the given polynomial, divide
the polynomial by its GCF, the resulting quotient is
the other factor.
The factored form of
12x3y5 – 20x5y2z is
4x3y2(3y3 – 5x2z)
2. Factor: 12x5y4 – 16x3y4 + 28x6
Steps 1:
Find the greatest common factor of the numerical
coefficients.
Factor:
12 = 3.4
16 = 4.4
28 = 7.4
The GCF of 12, 16 and 28 is 4.
2. Factor: 12x5y4 – 16x3y4 + 28x6
Steps 2:
Find the variable with the least exponent that
appears in each term of the polynomial.
x is common to all terms and 3 is the smallest
exponent for x . thus, x3
is the GCF of the variables.
2. Factor: 12x5y4 – 16x3y4 + 28x6
Steps 3:
The product of the greatest common factor in steps
(1) and (2) is the GCF of the polynomial.
4x3
is the GCF of 12x5y4 – 16x3y4 + 28x6
2. Factor: 12x5y4 – 16x3y4 + 28x6
Steps 4:
To completely factor the given polynomial, divide
the polynomial by its GCF, the resulting quotient is
the other factor.
The factored form of
12x5y4 – 16x3y4 + 28x6 is
4x3(3x2y4 – 4y4 +7x3)
Direction: Factor the following.
1. 15x2y + 20xy2
2. 14x4y2 – 21x3y5
3. 32a6b6 + 72a7b5
4. -30m4n3 + 40m5n4
5. 90x5y5 – 99x6y6
6. 30a7b8 – 18a8b6 – 6a7b7
7. -36p3q4 + 60p2q3 – 84p3q5
8. 4y3 – 20y2 + 24y
9. 16p2r5 + 48p3r6 – 24p4
10. 45a6b3 – 60a4b2 + 75a3b4
ACTIVITY 3: To Do…
Learning Resources:
Grade 8 Math Time
k-to-12-grade-8-math-learner-module

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common monomial factor

  • 2. Jessebel G. Bautista Antonio J. Villegas Voc’l High School My Profile
  • 3. Objectives: –recall GCF –factor polynomials whose terms have common monomial factor –think deductively using ECM –relate factoring in real life
  • 4. Drill: Give the greatest common factor (CGF) of the following expressions. 1. 12, 15, 18 2. 24, 36, 72 3. x3, x2, x 4. x2y2, xy4, x2y2 5. 5a3, 10a2, 15a 6. 30b4, 45b2, 60b3 7. 24x2y2, 40x2y3, 48xy4 8. 100m6n8,125m3n5, 250mn 9. (x -2y)4, (x - 2y)2, (x - 2y) 10. 12(a + b)5, 36(a + b)3, 48(a + b)
  • 5. Activity 1 FINDING COMMON Description: Your task in this activity is to identify common things that are present in the three pictures. Questions: 1. What are the things common to these pictures? 2. Are there things that make them different? 3. Can you spot things that are found on one picture but not on the other two? 4. What are the things common to two pictures but not on the other?
  • 6. The activity in the previous slides gave us the idea about the Greatest Common Monomial Factor. Now, on the next slide. Study the example of the ECM on how factoring the Greatest Common Monomial Factor is being done.
  • 7. Example – Conclusion Map (ECM) Direction: Let the students write the conclusion and their example given the ECM. Polynomial 6m + 8 GCF 2 Quotient of Polynomial 3m + 4 Factored Form 2 (3m +4) Polynomial 15x2+10 xy GCF 5x Quotient of polynomial 3x + 2y Factored Form 5x (3x +2y) Polynomial 5t4 + 4t3 + t2 GCF t2 Quotient of polynomial 5t2 + 4t + 1 Factored Form t2 (5t2 +4t + 1) Example 1 Example 2 Example 3 Conclusion Your own example
  • 9. 1. Factor : 12x3y5 – 20x5y2z Steps 1: Find the greatest common factor of the numerical coefficients. The GCF of 12 and 20 is 4.
  • 10. 1. Factor : 12x3y5 – 20x5y2z Steps 2: Find the variable with the least exponent that appears in each term of the polynomial. x and y are both common to all terms and 3 is the smallest exponent for x and 2 is the smallest exponent of y, thus, x3y2 is the GCF of the variables.
  • 11. 1. Factor : 12x3y5 – 20x5y2z Steps 3: The product of the greatest common factor in steps (1) and (2) is the GCF of the polynomial. 4x3y2 is the GCF of 12x3y5 – 20x5y2z.
  • 12. 1. Factor : 12x3y5 – 20x5y2z Steps 4: To completely factor the given polynomial, divide the polynomial by its GCF, the resulting quotient is the other factor. The factored form of 12x3y5 – 20x5y2z is 4x3y2(3y3 – 5x2z)
  • 13. 2. Factor: 12x5y4 – 16x3y4 + 28x6 Steps 1: Find the greatest common factor of the numerical coefficients. Factor: 12 = 3.4 16 = 4.4 28 = 7.4 The GCF of 12, 16 and 28 is 4.
  • 14. 2. Factor: 12x5y4 – 16x3y4 + 28x6 Steps 2: Find the variable with the least exponent that appears in each term of the polynomial. x is common to all terms and 3 is the smallest exponent for x . thus, x3 is the GCF of the variables.
  • 15. 2. Factor: 12x5y4 – 16x3y4 + 28x6 Steps 3: The product of the greatest common factor in steps (1) and (2) is the GCF of the polynomial. 4x3 is the GCF of 12x5y4 – 16x3y4 + 28x6
  • 16. 2. Factor: 12x5y4 – 16x3y4 + 28x6 Steps 4: To completely factor the given polynomial, divide the polynomial by its GCF, the resulting quotient is the other factor. The factored form of 12x5y4 – 16x3y4 + 28x6 is 4x3(3x2y4 – 4y4 +7x3)
  • 17. Direction: Factor the following. 1. 15x2y + 20xy2 2. 14x4y2 – 21x3y5 3. 32a6b6 + 72a7b5 4. -30m4n3 + 40m5n4 5. 90x5y5 – 99x6y6 6. 30a7b8 – 18a8b6 – 6a7b7 7. -36p3q4 + 60p2q3 – 84p3q5 8. 4y3 – 20y2 + 24y 9. 16p2r5 + 48p3r6 – 24p4 10. 45a6b3 – 60a4b2 + 75a3b4 ACTIVITY 3: To Do…
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  • 19. Learning Resources: Grade 8 Math Time k-to-12-grade-8-math-learner-module