What are the possible rational roots of f(x) = x4 – 173x3 – 16x2 – 7x – 15, according to the rational root theorem? “±” means “plus or minus”.Question 5Select one:a.{1, 3, 5, 15}b.{±1, ±3, ±5, ±15}c.{±1/15, ±3/15, ±1, ±3, ±5, ±15}d.{±1, ±5, ±1/3, ±5/3, ±1/5, ±1/15}e.None of these
Question
What are the possible rational roots of f(x) = x4 – 173x3 – 16x2 – 7x – 15, according to the rational root theorem? “±” means “plus or minus”.Question 5Select one:a.{1, 3, 5, 15}b.{±1, ±3, ±5, ±15}c.{±1/15, ±3/15, ±1, ±3, ±5, ±15}d.{±1, ±5, ±1/3, ±5/3, ±1/5, ±1/15}e.None of these
Solution
The possible rational roots of f(x) = x4 – 173x3 – 16x2 – 7x – 15, according to the rational root theorem, can be found by considering the factors of the constant term (-15) divided by the factors of the leading coefficient (1).
The factors of -15 are ±1, ±3, ±5, and ±15. The factors of 1 are ±1.
Combining these factors, we get the possible rational roots as ±1, ±3, ±5, and ±15.
Therefore, the correct answer is option b. {±1, ±3, ±5, ±15}.
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