Vedic Sutras:**[s1]: proportionally**** [s2]: first by first and last by last**

**Example 1**: E= 2x² + 7x +6

Split 7x = 3x+4x

First ratio of coefficient (2x²+3x) -> **2:3**

Last ratio of coefficient (4x+6) -> 4:6=**2:3**

=> 1st factor = (**2**x+**3**)

2nd factor:

2x²/(**2x**) +6/(**3**)= (x+2)

=> E = (2x+3).(x+2)

**Example 2**: Factorize E(x, y, z) = x²+xy-2y²+2xz -5yz-3z²

1. Let z =…

E’= x²+xy-2y² = (x+2y)(x-y)

2. Let y=0

E’= x²+2xz-3z² = (x+3z)(x-z)

=> E(x, y, z) = (x+2y+3z)(x-y-z)

**Example 3**: P(x, y, z) = 3x² + 7xy + 2y² +11xz + 7yz + 6z² *+ 14x + 8y + 14z + 8*

1. Eliminate y=z=0, retain x:

P = 3x²+14x+8= (x+4)(3x+2)

2. Eliminate…

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