Polynomial ring

If p is a prime in R, then p[x] is a prime in R[x], and
p[x] ∩ R = p. Hence if p₁ ⊂ p₂ strictly,
then p₁[x] ⊂ p₂[x] strictly. Also, p[x] + (x) is a prime in R[x].
If Q is a maximal ideal in R[x], then Q ∩ R is a maximal ideal in R.