# Basis and Dimension of P2

## Homework Statement

Find the basis and dimension of the following subspace U of P2

p(x) $$\ni$$ P2 such that p(1) = p(2)

## The Attempt at a Solution

I know all quadratics are in the form ax2 + bx + c

set p(2) = p(1)

4a + 2b + c = a + b + c
b = -3a

Therefore ax2 -3a + c

Basis(U) = a(x2-3x) + c

Therefore dim(U) = 2

I'm just wondering if I have the correct answer or not. Going into linear algebra midterm tomorrow and prof never really went over polynomials but it's on the test.

The basis for U is by the way $$\{x^2-3x,1\}$$. What you wrote down doesn't make much sense to me...