Chapter 6 - Vector Spaces - 6.2 Linear Independence, Basis, and Demension - Exercises for 6.2 - Page 457: 25

This set is not linearly independent.

The vector space $\mathcal{P}_2$ has dimension $3$, so any subset of $\mathcal{P}_2$ of cardinality greater than $3$ must be linearly dependent. Since $\mathcal{B}$ has size $4$, which is greater than $3$, $\mathcal{B}$ cannot be linearly independent.