Master Product

1. Master Product A technique for factoring trinomials Lutheran High Westland Mathematics Department by way of Martin Luther High School Mathematics Department by way of A Catholic Nun

2. Background Information • Used to factor quadratics in the form of ax2 + bx + c • For example: 3x2 – 4x + 5 a = 3 b = -4 c = 5 • This technique helps minimize the use of “guess and check” • You’re going to love this! Yeah, Right!!!!

3. The Master Product Technique • Ten sample problems will be presented with explanation of the steps. • Don’t be intimidated. Practice makes this technique easy to remember!

4. MP 12 Factor: 2x2 + 7x + 6 x 2x + 4 + 3 2 3 • Find a pair of factors for the MP whose sum is ‘b’ • Find the Master Product by multiplying ‘a’ by ‘c’ • Find a pair of factors for ‘a’ where each will factor one of the factors found in step 2. 1 2 • Write these factors with the variable in front of and opposite the numbers they factor from step 2. • Deflate: ‘4’ is replaced with ‘2’ as 4  2 is 2 ‘3’ is “replaced” with ‘3’ as 3  1 is 3 • Write your answer: (x + 2)(2x + 3)

5. MP 30 Factor: 3x2 – 17x + 10 x 3x - 15 - 2 5 2 • Find a pair of factors for the MP whose sum is ‘b’ • Find the Master Product by multiplying ‘a’ by ‘c’ • Find a pair of factors for ‘a’ where each will factor one of the factors found in step 2. 1 3 • Write these factors with the variable in front of and opposite the numbers they factor from step 2. • Deflate: ‘15’ is replaced with ‘5’ as 15  3 is 5 ‘2’ is “replaced” with ‘2’ as 2  1 is 2 • Write your answer: (x - 5)(3x - 2)

6. MP -40 Factor: 2x2 + 3x - 20 x 2x + 8 - 5 4 5 • Find a pair of factors for the MP whose sum is ‘b’ • Find the Master Product by multiplying ‘a’ by ‘c’ • Find a pair of factors for ‘a’ where each will factor one of the factors found in step 2. 1 2 • Write these factors with the variable in front of and opposite the numbers they factor from step 2. • Deflate: ‘8’ is replaced with ‘4’ as 8  2 is 4 ‘5’ is “replaced” with ‘5’ as 5  1 is 5 • Write your answer: (x + 4)(2x - 5)

7. MP -24 Factor: 3x2 - 23x - 8 x 3x - 24 + 1 8 1 • Find a pair of factors for the MP whose sum is ‘b’ • Find the Master Product by multiplying ‘a’ by ‘c’ • Find a pair of factors for ‘a’ where each will factor one of the factors found in step 2. 1 3 • Write these factors with the variable in front of and opposite the numbers they factor from step 2. • Deflate: ‘24’ is replaced with ‘8’ as 24  3 is 8 ‘1’ is “replaced” with ‘1’ as 1  1 is 1 • Write your answer: (x - 8)(3x + 1)

8. MP 10 Factor: x2 - 7x + 10 x x - 5 - 2 5 2 • Find a pair of factors for the MP whose sum is ‘b’ • Find the Master Product by multiplying ‘a’ by ‘c’ • Find a pair of factors for ‘a’ where each will factor one of the factors found in step 2. 1 1 • Write these factors with the variable in front of and opposite the numbers they factor from step 2. • Deflate: ‘5’ is replaced with ‘5’ as 5  1 is 5 ‘2’ is “replaced” with ‘2’ as 2  1 is 2 • Write your answer: (x - 5)(x - 2)

9. MP -21 Factor: x2 - 4x - 21 x x - 7 + 3 7 3 • Find a pair of factors for the MP whose sum is ‘b’ • Find the Master Product by multiplying ‘a’ by ‘c’ • Find a pair of factors for ‘a’ where each will factor one of the factors found in step 2. 1 1 • Write these factors with the variable in front of and opposite the numbers they factor from step 2. • Deflate: ‘7’ is replaced with ‘7’ as 7  1 is 7 ‘3’ is “replaced” with ‘3’ as 3  1 is 3 • Write your answer: (x - 7)(x + 3)

10. MP -126 Factor: 6x2 - 5x - 21 3x 2x - 14 + 9 7 3 • Find a pair of factors for the MP whose sum is ‘b’ • Find the Master Product by multiplying ‘a’ by ‘c’ • Find a pair of factors for ‘a’ where each will factor one of the factors found in step 2. 3 2 • Write these factors with the variable in front of and opposite the numbers they factor from step 2. • Deflate: ‘14’ is replaced with ‘7’ as 14  2 is 7 ‘9’ is replaced with ‘3’ as 9  3 is 3 • Write your answer: (3x - 7)(2x + 3)

11. MP 12 Factor: 6x2 + 7x + 2 3x 2x + 4 + 3 2 1 • Find a pair of factors for the MP whose sum is ‘b’ • Find the Master Product by multiplying ‘a’ by ‘c’ • Find a pair of factors for ‘a’ where each will factor one of the factors found in step 2. 3 2 • Write these factors with the variable in front of and opposite the numbers they factor from step 2. • Deflate: ‘4’ is replaced with ‘2’ as 4  2 is 2 ‘3’ is replaced with ‘1’ as 3  3 is 1 • Write your answer: (3x + 2)(2x + 1)

12. MP 100 Factor: 4x2 + 20x + 25 2x 2x + 10 + 10 5 5 • Find a pair of factors for the MP whose sum is ‘b’ • Find the Master Product by multiplying ‘a’ by ‘c’ • Find a pair of factors for ‘a’ where each will factor one of the factors found in step 2. 2 2 • Write these factors with the variable in front of and opposite the numbers they factor from step 2. • Deflate: ‘10’ is replaced with ‘5’ as 10  2 is 5 ‘10’ is replaced with ‘5’ as 10  2 is 5 • Write your answer: (2x + 5)(2x + 5)

13. MP -100 Factor: 4x2 - 25 2x 2x + 10 - 10 5 5 • Find a pair of factors for the MP whose sum is ‘b’ • Find the Master Product by multiplying ‘a’ by ‘c’ • Find a pair of factors for ‘a’ where each will factor one of the factors found in step 2. 2 2 • Write these factors with the variable in front of and opposite the numbers they factor from step 2. • Deflate: ‘10’ is replaced with ‘5’ as 10  2 is 5 ‘10’ is replaced with ‘5’ as 10  2 is 5 • Write your answer: (2x + 5)(2x - 5)

14. Happy Factoring!