What are the simplest factors of x^3 - 13x + 12

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The simplest factors of the expression x^3 - 13x + 12 have to be determined.

As the numeric coefficient of x^3 - 13x + 12 is 12, the products of the roots of x^3 - 13x + 12 = 0 is 12.

One of the likely factors could be 3.

x^3 - 13x + 12

=> x^3 - 3x^2 + 3x^2 - 9x - 4x + 12

=> x^2(x - 3) + 3x(x - 3) - 4(x - 3)

=> (x -3)(x^2 + 3x - 4)

=> (x -3)(x^2 + 4x - x - 4)

=> (x -3)(x(x + 4) - 1(x + 4))

=> (x - 3)(x - 1)(x + 4)

The factorized form of x^3 - 13x + 12 is (x - 3)(x - 1)(x + 4)

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