14. To prove the Rational Zeros Test, we assume the Fundamental Theorem of Arithmetic, which states...

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14. To prove the Rational Zeros Test, we assume the Fundamental Theorem of Arithmetic, which states that "Every integer has a unique prime factorization." Supply reasons for each step in the following proof (F is a polyno- mial function of order n with integer coefficients and non- zero constant): P (i) F F(²). = 0 and is in lowest terms. 9 an (2)" (ii) an P (¹¹ 9 + an-1 + + a + ao = 0 (iii) anp" + an-1pq++ a₁pq"-1 + aoq" = 0 (iv) anp" + an-1pq+...+ a₁pq"-1 = -aq" a₁pq"- + € 14. To prove the Rational Zeros Test, we assume the Fundamental Theorem of Arithmetic, which states that "Every integer has a unique prime factorization." Supply reasons for each step in the following proof (F is a polyno- mial function of order n with integer coefficients and non- zero constant): P (i) F F(²). = 0 and is in lowest terms. 9 an (2)" (ii) an P (¹¹ 9 + an-1 + + a + ao = 0 (iii) anp" + an-1pq++ a₁pq"-1 + aoq" = 0 (iv) anp" + an-1pq+...+ a₁pq"-1 = -aq" a₁pq"- + €

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We are given that Fx is a polynomial function with integer coefficients and a nonzero constant term ... View the full answer