Please show work. Find all possible rational zeros for the polynomial function.

Question

Please show work.

Find all possible rational zeros for the polynomial function. P(x) = 22x^3 - 32x^2 + 48x - 15 Choose the correct answer. A. plusminus 22/15, plusminus 11/15, plusminus 2/15, plusminus 15, plusminus 22/5, plusminus 11/5, plusminus 2/5, plusminus 5 plusminus 22/3, plusminus 2/3, plusminus 3, plusminus 1/15, plusminus 1/5, plusminus 1/3 plusminus 1 B. 15/22, 15/11, 15/2, 15, 5/22, 5/11, 5/2, 5, 3/22, 3/11, 3/2, 3, 1/22, 1/11, 1/2, 1 C. plusminus 15/22, plusminus 15/11, plusminus 15/2, plusminus 15, plusminus 5/22, plusminus 5/11, plusminus 5/2, plusminus 5, plusminus 3/22, plusminus 3/11, plusminus 3/2, plusminus 3, plusminus 1/22, plusminus 1/11, plusminus 1/2, plusminus 1

Explanation / Answer

Option C) is correct.

Given Polynomial is 22x^3 - 32x^2 + 48x - 15

Since all coefficients are integer, we can apply Rational Zeros Theorem.

Trailing coefficient (coefficient of the constant term) is 15

Find its factors (with plus and minus): ±1,±3,±5,±15. These are the possible values for p.

Leading coefficient (coefficient of the term with the highest degree) is 22.

Find its factors (with plus and minus): ±1,±2,±11,±22. These are the possible values for q.

Find all possible values of pq: ±1/1, ±1/2, ±1/11, ±1/22, ±3/1, ±3/2, ±3/11, ±3/22, ±5/1, ±5/2, ±5/11, ±5/22, ±15/1, ±15/2, ±15/11, ±15/22

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