1. The problem statement, all variables and given/known data Let be T : ℙ2 → ℙ2 a polynomial transformation (degree 2) Defined as T(a+bx+cx²) = (a+1) + (b+1)x + (b+1)x² It is a linear transformation? 2. Relevant equations A transformation is linear if T(p1 + p2) = T(p1) + T(p2) And T(cp1)= cT(p1) for any scalar c 3. The attempt at a solution Let p1=(a+bx+cx²) and p2=(d+ex+fx²) degree 2 polynomials T(p1+p2)= (a+d+1) + (b+e+1)x + (b+e+1)x² However T(p1) + T(p2)=[(a+1)+(d+1)] + [(b+1)+(e+1)]x + [(b+1)+(e+1)]x² T(p1) + T(p2)=(a+d+2) + (b+e+2)x + (b+e+1)x² So T(p1+p2) ≠ T(p1) + T(p2) Making it non linear transformation. Yet, my answer key says it is linear, either the key is wrong or there is something here I am not understanding. Any advise would be appreciated.