Is xp(x) in the Range of T for Given Polynomials?

[derryck1234]

Homework Statement

Let T: P2-P3 be the linear transformation defined by T(p(x)) = xp(x). Which of the following are in R(T)?

(a) x²
(b) 0
(c) 1 + x

Homework Equations

R(T) is the the set of all vectors in P3 which are images under T of vectors in P2.

The Attempt at a Solution

I just don't know where to start? I don't know what p(x) is?

 

[Mark44]

Homework Statement

Let T: P2-P3 be the linear transformation defined by T(p(x)) = xp(x). Which of the following are in R(T)?

(a) x²
(b) 0
(c) 1 + x

Homework Equations

R(T) is the the set of all vectors in P3 which are images under T of vectors in P2.

The Attempt at a Solution

I just don't know where to start? I don't know what p(x) is?

Start with how the definitions of P₂ and P₃.

p(x) is an arbitrary function in P₂.