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1. Let V={(X^2+X+1)p(x) : p(x) [itex]\in[/itex] P2(x)}

Show that V is a subspace of P4(x). Display a basis, with a proof. What is the dimension of V?

2.

3. I started to try to figure out how to prove that V is a subspace of P4, but I'm not sure how.

To show that it is closed under addition:

p(x)=x^2 is in P2(x)

(x^2+x+1)(x^2)+(a^2+a+1)(a^2)

x^4+x^3+x^2+a^4+a^3+a^2 is in P4, because no exponent is greater than 4.

The zero vector is if p(x) = 0

And then I'm not sure how to show that multiplication is closed

Show that V is a subspace of P4(x). Display a basis, with a proof. What is the dimension of V?

2.

3. I started to try to figure out how to prove that V is a subspace of P4, but I'm not sure how.

To show that it is closed under addition:

p(x)=x^2 is in P2(x)

(x^2+x+1)(x^2)+(a^2+a+1)(a^2)

x^4+x^3+x^2+a^4+a^3+a^2 is in P4, because no exponent is greater than 4.

The zero vector is if p(x) = 0

And then I'm not sure how to show that multiplication is closed

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