Problem 5: Consider the following polynomials in the space P₁(R) P(x)=1+2x-1² + 21³ P₂(1)=1+1-1² + 1ª + 2ª P3(1)=1+31-1² + 3r³ − 1ª P₁(1)=-1+1² a) Is the polynomial q(x)=1+x²+2r³ in Span (p₁(1), P2(1), Ps(2), P₁(1)}? b) Find a basis for Span{pi(x), Pa(z), P3(1), P4(1)}.

Fig: 1