Is the set of all polynomials px in Pn so that p0 0 a subsp

Is the set of all polynomials p(x) in P_n so that p(0) = 0 a subspace of P_n? Justify!

Yes it will be a subspace

1. 0 belongs to this set

2. Let, p,q be two polynomials in this set

(p+q)(0)=p(0)+q(0)=0

So,p+q is also in this set

3. Let, p be a polynomial in this set and c be a real number

(cp)(0)=cp(0)=0

So,cp is also in this set

Hence proved