Please fully factorize these equations:

1. \(36x^3 - 6x\)
2. \(12x^3 + 15x^2\)
3. \(8x - 10x^2\)

36 x 3 − 6 x = 6 x ( 6 x 2 − 1 ) = 6 x [( x 6 ​ ) 2 − 1 2 ] = 6 x ( x 6 ​ − 1 ) ( x 6 ​ + 1 ) 12 x 3 + 15 x 2 = 3 x 2 ( 4 x + 5 ) 8 x − 10 x 2 = 2 x ( 4 − 5 x )

Answered by Anonymous | 2024-06-10

1 ) 36 x 3 − 6 x = 6 x ( 6 x 2 − 1 ) = 6 x [( 6 ​ ⋅ x ) 2 − 1 2 ] = 6 x ( x 6 ​ − 1 ) ( x 6 ​ + 1 ) 2 ) 12 x 3 + 15 x 2 = 3 x 2 ( 4 x + 3 ) 3 ) 8 x − 10 x 2 = 2 x ( 4 − 5 x )

Answered by kate200468 | 2024-06-10

The factorizations of the equations are as follows: 1) 36 x 3 − 6 x = 6 x ( 6 ​ x − 1 ) ( 6 ​ x + 1 ) , 2) 12 x 3 + 15 x 2 = 3 x 2 ( 4 x + 5 ) , 3) 8 x − 10 x 2 = 2 x ( 4 − 5 x ) . Each equation was simplified by identifying the greatest common factors and applying factoring techniques. The final results represent the fully factored forms of each polynomial.
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Answered by Anonymous | 2024-12-23