(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Determine whether the following is a subspace of [tex]P_{4}_[/tex]

(a) The set of polynomials in [tex]P_{4}[/tex] of even degree.

2. Relevant equations

[tex]P_{4} = ax^{3}+bx^{2}+cx+d[/tex]

3. The attempt at a solution

[tex](p+q(x)) = p(x) + q(x)[/tex]

[tex](\alpha p)(x) = p(\alpha x)[/tex]

If p and q are both of degree 2 then both scalar multiplication and vector addition should return a polynomial of degree 2 as far as I can tell, however my book states that this is not a subspace of [tex]P_{4}[/tex]. I can't tell why it wouldn't be.

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# Homework Help: Subspace of P4 problem

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