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MATHEMATICS:
Factoring Polynomials with Common Monomial Factor How can I factor polynomials with common monomial factor? LESSON 001
GRADE 08
ALGEBRA
A.Unlocking Key Concepts
COMMON MONOMIAL FACTOR
A.COMMON
common means “shared” between two different things. Anong meron sa isa, na meron sa isa?
B.MONOMIAL
A polynomial with ONLY one term. Kapag yung polynomial ay walang addition or subtraction operation.
C.FACTOR
A number or an algebraic expression that divides another number or expression evenly.
GENERAL DEFINITION
TRY THESE!
a. 54 and 99
b. 32 and 64
c. 30 and 100
85.87 cm
GRADE 08 MATHEMATICS: ALGEBRA Factoring Polynomials with Common Monomial Factor
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Ano yung mga number/s
expression na pwedeng i-divide sa
numero
or
isang
or expression?
A.Unlocking Key Concepts
ANSWERS: TRY THESE! a. 54 and 99
TO FIND THE GCF? (Example: 65 & 25)
Step 1: Write down all the Positive Factors of a given constant/ number Everything should be a whole number Step 2: Determine the Greatest (Pinakamataas) Common (Pareho) Factor between the two constants/numbers 54: 1 2 3 6 9 18 27 57 99: 1 3 9 11 33 99 b. 32 and 64 32: 1 2 4 8 16 32 64: 1 2 4 8 18 32 64 c. 30 and 100 30: 1 2 3 5 6 10 15 30 100: 1 2 4 5 10 20 25 50 100 65: 1 5 13 65 25: 1 5 25 65: 1 5 13 65 25: 1 5 25 GCF: 5 GCF: 9 GCF: 32 GCF: 10
PROCEDURES
1: STEP 2:
3:
4: GRADE 08 MATHEMATICS: ALGEBRA Factoring Polynomials with Common Monomial Factor https://www.facebook.com/jmathsinc/ https://issuu.com/mathmadeeasyph jmathsph@gmail.com
HOW
REMEMBER
GENERAL
STEP
STEP
STEP
https://www.facebook.com/jmathsinc/ https://issuu.com/mathmadeeasyph jmathsph@gmail.com GRADE 08 MATHEMATICS: ALGEBRA Factoring Polynomials with Common Monomial Factor
STEP 1 STEP 2 STEP 3 STEP 4 Solving the GCF Expanding each Variable Determining Common Factors Common Monomial Factor 25x2 1, 5, 25 x • x x • x 5x 55x3 1, 5, 11, 55 x • x • x x • x • x 60x 1, 2, 3, 4, 5, 12, 15, 20, 30, 60 x x TERM STEP 1 STEP 2 STEP 3 STEP 4 Solving the GCF Expanding each Variable Determining Common Factors Common Monomial Factor x5y 1 x • x • x • x • x • y x • x • x • x • x • y 1x2 or x2 18x4y3 1, 2, 3, 6, 9, 18 x • x • x • x • y • y • y x • x • x • x • y • y • y 14x2y2 1, 2, 7, 14 x • x • y • y x • x • y • y 10x5 1, 2, 5, 10 x • x • x • x • x x • x • x • x • x EXAMPLES
A.Unlocking Key Concepts TRY THESE! TERM
A.Unlocking Key Concepts
EXAMPLES
TERM STEP 1 STEP 2 STEP 3 STEP 4 Solving the GCF Expanding each Variable Determining Common Factors Common Monomial Factor 75x4zy3 1, 3, 5, 15, 25, 75 x • x • x • x • z • y • y • y x • x • x • x • z • y • y • y 25x2zy2 25x2z5y2 1, 5, 25 x • x • z • z • z • z • z • y • y x • x • z • z • z • z • z • y • y 50x2z4y4 1, 2, 5, 10, 25, 50 x • x • z • z • z • z • y • y • y • y x • x • z • z • z • z • y • y • y • y TERM STEP 1 STEP 2 STEP 3 STEP 4 Solving the GCF Expanding each Variable Determining Common Factors Common Monomial Factor 15s2t2v 1, 3, 5, 15 s • s • t • t • v s • s • t • t • v 1 45s4t 1, 3, 5, 9, 15, 45 s • s • s • s • t s • s • s • s • t 8v 1, 2, 4, 8 v v 19s2t2 1, 19 s • s • t • t s • s • t • t GRADE 08 MATHEMATICS: ALGEBRA Factoring Polynomials with Common Monomial Factor https://www.facebook.com/jmathsinc/ https://issuu.com/mathmadeeasyph jmathsph@gmail.com
TRY THESE!
https://www.facebook.com/jmathsinc/ https://issuu.com/mathmadeeasyph jmathsph@gmail.com GRADE 08 MATHEMATICS: ALGEBRA Factoring Polynomials with Common Monomial Factor B.Introducing New Concepts NEW CONCEPTS What is Factoring? FACTORING x2+5x+6 (x+3)(x+2)
B.Introducing New Concepts What are the Importance of Factoring? GRADE 08 MATHEMATICS: ALGEBRA Factoring Polynomials with Common Monomial Factor https://www.facebook.com/jmathsinc/ https://issuu.com/mathmadeeasyph jmathsph@gmail.com
B.Introducing New Concepts
Factoring Polynomials with Common Monomial Factor
STEPS
Step 1: Determine the Common Monomial Factors on all the terms of the given Polynomial Write the CMF in a Parenthesis This will be the First Factor of the Polynomial Step 2: For the Second Factor, this involves Division of Polynomials. Divide each term to the CMF Step 3: Write down all the quotients in another parenthesis beside the first factor This will be considered as the second factor
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ON FACTORING POLYNOMIALS WITH COMMON MONOMIAL FACTORS REMEMBER
EXAMPLES S T E P 1 TERM Solving the GCF Expanding each Variable Determining Common Factors Common Monomial Factor 2x2 1, 2 x • x x • x 2x 12xy 1, 2, 3, 4, 6, 12 x • y x • y 6x 1, 2, 3, 6 x x S T E P 2 TERM Dividing Each Term with CMF Quotient 2��2 2��2 2x �� 12���� 12���� 2�� 6�� 6x 6�� 2�� 3 S T E P 3 =(2��)(��−6��+3) =2��2 12����+6��
B.Introducing New Concepts
TRY THESE!
EXAMPLES 35��2��2 5���� 12��2��3��3��2 +8������3 6��4 −10��3 +2�� 8��5 −20��4 −12��2 −3��4 +15��2 +6�� 5ℎ3��−20ℎ2��2 +100ℎ�� =35��2��2 5���� =(5����)( ) = 35��2��2 5���� =7���� = 5���� 5���� = 1 =(5����)(7���� 1) =6��4 −10��3 +2�� =2��( ) = 6��4 2�� =3��3 = −10��3 2�� = 5��2 = 2�� 2�� =1 =2��(3��3 5��2 +1) = 3��4 +15��2 +6�� =(3��)( ) = −3��4 3�� = ��3 = 15��2 3�� =5�� = 6�� 3�� =2 =(3��)( ��3 +5��+2) =12��2��3��3��2 +8������3 =(4������2)( ) = 12��2��3��3��2 4������2 =3����2��3 = 8������3 4������2 =2�� =(4������2)(3����2��3 +2��) =8��5 20��4 12��2 =(2��2)( ) = 8��5 2��2 =4��3 = 20��4 2��2 = 10��2 = −12��2 2��2 = 6 =(2��2)(4��3 10��2 6) =5ℎ3�� 20ℎ2��2 +100ℎ�� =5ℎ��( ) = 5ℎ3�� 5ℎ�� =ℎ2 = 20ℎ2��2 5ℎ�� =−4ℎ�� = 100ℎ�� 5ℎ�� =20 =5ℎ��(ℎ2 4ℎ��+20) GRADE 08 MATHEMATICS: ALGEBRA Factoring Polynomials with Common Monomial Factor https://www.facebook.com/jmathsinc/ https://issuu.com/mathmadeeasyph jmathsph@gmail.com
GRADE 08 MATHEMATICS: ALGEBRA Factoring Polynomials with Common Monomial Factor
C. More Examples
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ACTIVITY
Given Factors 1. 16��4 +4��3 2. 9��+36 3. 63+45�� 4. 6��3 3��5 5. 6��5 6��4 6. 63��12 35��6 7. 14��+21��2 +21��3 8. 10��3 9��2 +�� 9. 28��2 8�� 36 10. 8��7 +24��6 +12��5 Given Factors 11. 20 35��2 20��3 12. 9��6 63��3 90��2 13. 3��3 +15��2 6�� 14. 50��3 +50��2 20 15. 32��3 +28�� 20 16. 90��5 +100��+60 17. 3��2 +9��+27 18. 12��2 +4�� 12 19. 64+40��2 +72�� 20. 18��2 +15�� 15
TRY THESE!
ANSWER
Given Factors 1. 16��4 +4��3 ������ ����+�� 2. 9��+36 (��)(��+��) 3. 63+45�� (��)(��+����) 4. 6��3 3��5 ������ �� ���� 5. 6��5 6��4 ������ ��+�� 6. 63��12 35��6 ������ ������ �� 7. 14��+21��2 +21��3 ���� ��+����+������ 8. 10��3 9��2 +�� �� �������� ����+�� 9. 28��2 8�� 36 ( ��)(������ +����+��) 10. 8��7 +24��6 +12��5 ������ ( ������ +����+��) Given Factors 11. 20 35��2 20��3 �� �� ������ ������ 12. 9��6 63��3 90��2 ������ ���� ���� ���� 13. 3��3 +15��2 6�� (����)( ���� +���� ��) 14. 50��3 +50��2 20 (����)(������ +������ ��) 15. 32��3 +28�� 20 (��)(������ +���� ��) 16. 90��5 +100��+60 (����)( ������ +������+��) 17. 3��2 +9��+27 (��)(���� +����+��) 18. 12��2 +4�� 12 (��)(������ +�� ��) 19. 64+40��2 +72�� (��)(��+������ +����) 20. 18��2 +15�� 15 (��)( ������ +���� ��) GRADE 08 MATHEMATICS: ALGEBRA Factoring Polynomials with Common Monomial Factor https://www.facebook.com/jmathsinc/ https://issuu.com/mathmadeeasyph jmathsph@gmail.com
C. More Examples
KEY TRY THESE!
https://www.facebook.com/jmathsinc/ https://issuu.com/mathmadeeasyph 85.87 cm jmathsph@gmail.com GRADE 08 MATHEMATICS: ALGEBRA Factoring Polynomials with Common Monomial Factor How can I factor polynomials with common monomial factor? LESSON 001 Written, Prepared, and Edited by: John michael s. cariazo, lpt
