Answer :
By applying the Rational Root Theorem, you can factorize the given polynomial as (x + 3)(x - 2)(x - 4)(x^2 - 4x + 2). This theorem helps identify potential rational roots of the polynomial.
In this problem, we are using the Rational Root Theorem to factor the given polynomial equation, x^5 - 8x^4 - 39x^3 + 326x^2 + 140x - 1176.
The Rational Root Theorem states that if a polynomial has a rational root, p/q, then p is a factor of the constant term, and q is a factor of the leading coefficient.
In our case, the constant term is -1176 and the leading coefficient is 1. So, potential rational roots for this polynomial are p/q such that p is a factor of -1176 and q is a factor of 1.
By trial-and-error, you can find that x = -3, x = 2, and x = 4 are roots of the polynomial.
Therefore, the polynomial factors as (x + 3)(x - 2)(x - 4)(x^2 - 4x + 2). The last factor is a quadratic and does not have rational roots, so the factorization is complete.
Learn more about Rational Root Theorem here:
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