Please show all work step by step and as legible as possible! Thank you so much!

5. [8] Show that P2 is a subspace of P3 (See Problem #1 for the definition of the polynomial vector spaces.) 6. [8] Do the polynomials t3 + t + 2, t2 - t + 2, t3 + 2, and -t3 + t2 - 5t + 3 span P3? (Give support for your conclusion.)