A technique for factoring trinomials

Lutheran High Westland Mathematics DepartmentLutheran High Westland Mathematics Department

by way ofby way of

Martin Luther High School Mathematics DepartmentMartin Luther High School Mathematics Department

by way ofby way of

A Catholic NunA Catholic Nun

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!

Ten sample problems will be presented with explanation of the steps.

Don’t be intimidated. Practice makes this technique easy to remember!

1. Find the Master Product by multiplying ‘a’ by ‘c’

MP

12

+ 4

+ 32. Find a pair of factors for the

MP whose sum is ‘b’

3. Find a pair of factors for ‘a’ where each will factor one of the factors found in step 2.

4. Write these factors with the variable in front of and opposite the numbers they factor from step 2.

5. Deflate: ‘4’ is replaced with ‘2’ as 4 2 is 2 ‘3’ is “replaced” with ‘3’ as 3 1 is 3

6. Write your answer: (x + 2)(2x + 3)

x

2x

/ 2

/ 3

1

2

1. Find the Master Product by multiplying ‘a’ by ‘c’

MP

30

- 15

- 22. Find a pair of factors for the

MP whose sum is ‘b’

3. Find a pair of factors for ‘a’ where each will factor one of the factors found in step 2.

4. Write these factors with the variable in front of and opposite the numbers they factor from step 2.

5. Deflate: ‘15’ is replaced with ‘5’ as 15 3 is 5 ‘2’ is “replaced” with ‘2’ as 2 1 is 2

6. Write your answer: (x - 5)(3x - 2)

x

3x

/ 5

/ 2

1

3

1. Find the Master Product by multiplying ‘a’ by ‘c’

MP

-40

+ 8

- 52. Find a pair of factors for the

MP whose sum is ‘b’

3. Find a pair of factors for ‘a’ where each will factor one of the factors found in step 2.

4. Write these factors with the variable in front of and opposite the numbers they factor from step 2.

5. Deflate: ‘8’ is replaced with ‘4’ as 8 2 is 4 ‘5’ is “replaced” with ‘5’ as 5 1 is 5

6. Write your answer: (x + 4)(2x - 5)

x

2x

/ 4

/ 5

1

2

1. Find the Master Product by multiplying ‘a’ by ‘c’

MP

-24

- 24

+ 12. Find a pair of factors for the

MP whose sum is ‘b’

3. Find a pair of factors for ‘a’ where each will factor one of the factors found in step 2.

4. Write these factors with the variable in front of and opposite the numbers they factor from step 2.

5. Deflate: ‘24’ is replaced with ‘8’ as 24 3 is 8 ‘1’ is “replaced” with ‘1’ as 1 1 is 1

6. Write your answer: (x - 8)(3x + 1)

x

3x

/ 8

/ 1

1

3

1. Find the Master Product by multiplying ‘a’ by ‘c’

MP

10

- 5

- 22. Find a pair of factors for the

MP whose sum is ‘b’

3. Find a pair of factors for ‘a’ where each will factor one of the factors found in step 2.

4. Write these factors with the variable in front of and opposite the numbers they factor from step 2.

5. Deflate: ‘5’ is replaced with ‘5’ as 5 1 is 5 ‘2’ is “replaced” with ‘2’ as 2 1 is 2

6. Write your answer: (x - 5)(x - 2)

x

x

/ 5

/ 2

1

1

1. Find the Master Product by multiplying ‘a’ by ‘c’

MP

-21

- 7

+ 32. Find a pair of factors for the

MP whose sum is ‘b’

3. Find a pair of factors for ‘a’ where each will factor one of the factors found in step 2.

4. Write these factors with the variable in front of and opposite the numbers they factor from step 2.

5. Deflate: ‘7’ is replaced with ‘7’ as 7 1 is 7 ‘3’ is “replaced” with ‘3’ as 3 1 is 3

6. Write your answer: (x - 7)(x + 3)

x

x

/ 7

/ 3

1

1

1. Find the Master Product by multiplying ‘a’ by ‘c’

MP

-126

- 14

+ 92. Find a pair of factors for the

MP whose sum is ‘b’

3. Find a pair of factors for ‘a’ where each will factor one of the factors found in step 2.

4. Write these factors with the variable in front of and opposite the numbers they factor from step 2.

5. Deflate: ‘14’ is replaced with ‘7’ as 14 2 is 7 ‘9’ is replaced with ‘3’ as 9 3 is 3

6. Write your answer: (3x - 7)(2x + 3)

3x

2x

/ 7

/ 3

3

2

1. Find the Master Product by multiplying ‘a’ by ‘c’

MP

-20

+10

- 22. Find a pair of factors for the

MP whose sum is ‘b’

3. Find a pair of factors for ‘a’ where each will factor one of the factors found in step 2.

4. Write these factors with the variable in front of and opposite the numbers they factor from step 2.

5. Deflate: ‘10’ is replaced with ‘5’ as 10 2 is 5 ‘-2’ is replaced with ‘1’ as -2 -2 is 1

6. Write your answer: (-2x + 5)(2x + 1)

-2x

2x

/ 5

/ +1

-2

2

1. Find the Master Product by multiplying ‘a’ by ‘c’

MP

100

+ 10

+ 102. Find a pair of factors for the

MP whose sum is ‘b’

3. Find a pair of factors for ‘a’ where each will factor one of the factors found in step 2.

4. Write these factors with the variable in front of and opposite the numbers they factor from step 2.

5. Deflate: ‘10’ is replaced with ‘5’ as 10 2 is 5 ‘10’ is replaced with ‘5’ as 10 2 is 5

6. Write your answer: (2x + 5)(2x + 5)

2x

2x

/ 5

/ 5

2

2

1. Find the Master Product by multiplying ‘a’ by ‘c’

MP

-100

+ 10

- 102. Find a pair of factors for the

MP whose sum is ‘b’

3. Find a pair of factors for ‘a’ where each will factor one of the factors found in step 2.

4. Write these factors with the variable in front of and opposite the numbers they factor from step 2.

5. Deflate: ‘10’ is replaced with ‘5’ as 10 2 is 5 ‘10’ is replaced with ‘5’ as 10 2 is 5

6. Write your answer: (2x + 5)(2x - 5)

2x

2x

/ 5

/ 5

2

2