S.O.S. Mathematics CyberBoard

If you have the following basis vectors for a polynomial vector space
c_1*[-1,1,0]
c_2*[-1,0,1]

then how do you get to the form

(x-1)
(x^2 - 1)

as representing the same basis?

Sometimes in 3d, people write the x,y,z unit vectors as i,j,k. So the vector (1,2,3) is 1 i + 2 j + 3 k.

In the vector space of polynomials of degree <= 2, the "natural" basis vectors are the polynomials { 1, x, x^2} and the vector (1,2,3) is 1 (1) + 2 (x) + 3(x^2) .

I don't see the connection between my post and your post...

(1,2,3) = 1(1) + 2(x) + 3(x^2) = x^2 + 2x + 1
(-1,1,0) = (-1)(1) + 1(x) + 0 (x^2) = x -1
(-1,0,1) = (-1)(1) = 0 (x) + 1 (x^2) = -1 + x^2 = x^2 - 1