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Answer :
Final answer:
The task involves finding the rational roots of a polynomial using the Rational Root Theorem and rewriting the polynomial in factored form.
Explanation:
The focus of this problem is to analyze the given polynomial, P(x) = 6x4 - 23x3 - 13x2 + 32x + 16, and to identify its rational zeros. To do this task, we will use the Rational Root Theorem which states that any rational root of the polynomial, expressed in lowest terms, has a numerator that is a factor of the constant term (in this case, 16) and a denominator that is a factor of the leading coefficient (in this case, 6). By simply listing down the possible factors, we can use synthetic division or direct substitution to test if they are indeed roots of the given polynomial. After identifying all rational roots, we then rewrite the polynomial in its factored form considering those roots.
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