common monomial factor

Grade 8 Mathematics
Quarter 1

1. Factors of Polynomials 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 . 12, 15, 18 24, 36, 72 x 3 , x 2 , x x 2 y 2 , xy 4 , x 2 y 2 5a 3 , 10a 2 , 15a 6. 30b 4 , 45b 2 , 60b 3 7. 24x 2 y 2 , 40x 2 y 3 , 48xy 4 8. 100m 6 n 8 ,125m 3 n 5 , 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 15x 2 +10 xy GCF 5x Quotient of polynomial 3x + 2y Factored Form 5x (3x +2y) Polynomial 5t 4 + 4t 3 + t 2 GCF t 2 Quotient of polynomial 5t 2 + 4t + 1 Factored Form t 2 (5t 2 +4t + 1) Example 1 Example 2 Example 3 Conclusion Your own example

8. Examples

9. 1. Factor : 12 x 3 y 5 – 20 x 5 y 2 z Steps 1: Find the greatest common factor of the numerical coefficients. The GCF of 12 and 20 is 4 .

10. 1. Factor : 12 x 3 y 5 – 20 x 5 y 2 z 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, x 3 y 2 is the GCF of the variables.

11. 1. Factor : 12 x 3 y 5 – 20 x 5 y 2 z Steps 3: The product of the greatest common factor in steps (1) and (2) is the GCF of the polynomial. 4x 3 y 2 is the GCF of 12x 3 y 5 – 20x 5 y 2 z.

12. 1. Factor : 12 x 3 y 5 – 20 x 5 y 2 z Steps 4: To completely factor the given polynomial, divide the polynomial by its GCF, the resulting quotient is the other factor. T he factored form of 12x 3 y 5 – 20x 5 y 2 z is 4x 3 y 2 (3y 3 – 5x 2 z)

13. 2. Factor: 12x 5 y 4 – 16x 3 y 4 + 28x 6 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 : 12x 5 y 4 – 16x 3 y 4 + 28x 6 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 , x 3 is the GCF of the variables.

15. 2. Factor : 12x 5 y 4 – 16x 3 y 4 + 28x 6 Steps 3: The product of the greatest common factor in steps (1) and (2) is the GCF of the polynomial. 4x 3 is the GCF of 12x 5 y 4 – 16x 3 y 4 + 28x 6

16. 2. Factor : 12x 5 y 4 – 16x 3 y 4 + 28x 6 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 12x 5 y 4 – 16x 3 y 4 + 28x 6 is 4x 3 (3x 2 y 4 – 4y 4 +7x 3 )

17. Direction: Factor the following. 15x 2 y + 20xy 2 14x 4 y 2 – 21x 3 y 5 32a 6 b 6 + 72a 7 b 5 -30m 4 n 3 + 40m 5 n 4 90x 5 y 5 – 99x 6 y 6 30a 7 b 8 – 18a 8 b 6 – 6a 7 b 7 -36p 3 q 4 + 60p 2 q 3 – 8 4 p 3 q 5 4y 3 – 20y 2 + 24y 16p 2 r 5 + 48p 3 r 6 – 24p 4 45a 6 b 3 – 60a 4 b 2 + 75a 3 b 4 ACTIVITY 3: To Do…

18. Learning Resources: Grade 8 Math Time k-to-12-grade-8-math-learner-module