Answer:
## Addition: P(x) + Q(x)
P(x)+Q(x) = X³ - 3X - 1 + X - 1
=X³ - 2X - 2
So P(x) + Q(x) = X³ - 2X - 2
## Subtraction: P(x) - Q(x)
P(x) - Q(x) = X³ - 3X - 1 - (X - 1)
= X³ - 3X - 1 - X + 1
= X³ - 4X
So P(x) - Q(x) = X³ - 4X
## Multiplication: P(x) × Q(x)
P(x) × Q(x) = (X³ - 3X - 1) × (X - 1)
= X⁴ - X³ - 3X² + 3X - X + 1
= X⁴ -X³ - 3X² + 2X + 1
So P(x) × Q(x) = X⁴ -X³ - 3X² + 2X + 1
