Question

Based on the rational root theorem, which of the following are possible roots of P(x) = x5 + 3x2 + 2x + 6?
Select all that apply

1/6

–2

1/3

1

–3

Answer 1

Rational Root Theorem: possible rational roots are p/q where p | 6 (constant) and q | 1 (leading coefficient), so possible values are ±1, ±2, ±3, ±6.

From the given list, the possible ones are: −2, 1, −3.

(These are only candidates — checking shows none of them actually makes P(x)=0: P(1)=12, P(−2)=−18, P(−3)=−216.)