High School Polynomial Space: Can Degree 2 Fit in 1+x^2?

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The polynomial (1 + x^2) cannot span the space of polynomials of degree 2 because it is a single polynomial. The space of degree 2 polynomials is three-dimensional, requiring at least three linearly independent polynomials to form a basis. Therefore, (1 + x^2) does not meet the criteria for spanning this space. A single polynomial lacks the necessary dimensions to represent all degree 2 polynomials. Thus, (1 + x^2) is insufficient for spanning the polynomial space of degree 2.
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Hi
The polynomial ( 1+x^2 )
Can this polynomial span the space of polynomials of degree 2 in standard basis ?
 
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No, it is a single polynomial. The space of polynomials of degree 2 is three-dimensional.
 

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