How can I factor: (x^3 - 7x^2 + 14x - 8)?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We have to factorize: x^3 - 7x^2 + 14x - 8

One way of doing this is provided.

x^3 - 7x^2 + 14x - 8

we can see that 8 = 2^3, this can be combined with x^3

=> x^3 - 8 - 7x^2 + 14x

use x^3 - y^3 = (x - y)(x^2 + xy + y^2)

=> (x - 2)(x^2 + 2x + 4) - 7x( x - 2 )

=> (x - 2)[x^2 + 2x + 4 - 7x]

=> (x - 2)[x^2 - 5x + 4]

=> (x - 2)[x^2 - 4x - x + 4]

=> (x - 2)[x(x - 4) - 1(x - 4)]

=> (x - 2)(x - 1)(x - 4)

The required factorization of x^3 - 7x^2 + 14x - 8 = (x - 2 )(x - 1)(x - 4)

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