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    The factors of polynomial x3−6x2+11x−6x^3 - 6x^2 + 11x - 6x3−6x2+11x−6​ are-
    Question

    The factors of polynomial x36x2+11x6x^3 - 6x^2 + 11x - 6​ are-

    A.

    (x + 1)(x + 2)(x - 3)

    B.

    (x - 1)(x + 2)(x - 3)

    C.

    (x - 1)(x - 2)(x - 3)

    D.

    (x - 1)(x - 2)(x + 3)

    Correct option is C

    Given:

    Polynomial: x³ - 6x² + 11x - 6
    We need to find its factors.

    Use Rational Root Theorem

    Try simple values like x = 1:

    1³ - 6(1)² + 11(1) - 6 = 1 - 6 + 11 - 6 = 0
    So, x = 1 is a root => (x - 1) is a factor

    Divide the polynomial by (x - 1)

    Use long division or synthetic division:
    x³ - 6x² + 11x - 6 ÷ (x - 1) = x² - 5x + 6

    Now factor x² - 5x + 6:
    = (x - 2)(x - 3)

    Final Factorization:
    x³ - 6x² + 11x - 6 = (x - 1)(x - 2)(x - 3)

    Correct Answer is (x - 1)(x - 2)(x - 3)

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