Question

According to the Rational Root Theorem, what are all the potential rational roots of f(x)=15x11–6x8+x3–4x3?

A) Plus-or-minus one-fifteenth
B) Plus-or-minus one-fifth
C) Plus-or-minus one-third
D) Plus-or-minus three-fifths
E) Plus-or-minus 1, plus-or-minus 3

Answer 1

Answer: (A)

Plus-or-minus one-fifthteenth, Plus-or-minus one-fifth, Plus-or-minus one-third, Plus-or-minus three-fifths, Plus-or-minus 1, Plus-or-minus3

Step-by-step explanation:

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Answer 2

The potential rational roots for the polynomial f(x)=15x^11−6x^8+x^3−4x^3 are plus-or-minus 1, plus-or-minus 1/3, plus-or-minus 1/5, and plus-or-minus 3/5, making the correct answer E) Plus-or-minus 1, plus-or-minus 3/5.

Step-by-step explanation:

According to the Rational Root Theorem, the potential rational roots of a polynomial are all possible fractions, positive and negative, that can be formed by dividing the factors of the constant term by the factors of the leading coefficient. In the polynomial f(x)=15x11−6x8+x3−4x3, the constant term is not explicitly given, implying it is 0. Therefore, we do not need to consider the factors of the constant term, only the factors of the leading coefficient, which is 15. Factors of 15 are ±1, ±3, ±5, and ±15. Thus, the possible rational roots are plus-or-minus 1, plus-or-minus 1/3, plus-or-minus 1/5, and plus-or-minus 3/5. Answer choices A, B, C, and D are subsets of this complete set, but the correct and complete answer is E) Plus-or-minus 1, plus-or-minus 3/5.