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Answer :
To factor the cubic polynomial [tex]15x^3-163x^2+257x-45[/tex], one should seek the roots of the polynomial and express it as the product of linear factors, potentially employing various algebraic techniques or numerical methods.
The factored form of 15x³-163x²+257x-45 is sought in the student's question. To find the factored form of this cubic polynomial, one must find its roots and express the polynomial as a product of its linear factors. This might involve techniques such as synthetic division, the rational root theorem, or numerical methods like the Newton-Raphson method if the roots are not readily apparent. The process can be time-consuming and may not yield factors with integer coefficients. It is important to note that while the polynomial is cubic (degree 3), it may not always be possible to factor it into linear factors over the integers or even over the real numbers; sometimes complex factors are necessary.
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