Let P2 be the vector space of all polynomials of degree ≤ 2 with coefficients in R, and S= {1 + 2x, 1 + 3x + 5x^2 , 4x + 5x^2 } .Is Span(S)= P2?

Elementary Linear Algebra (MindTap Course List)
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Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 47CR: Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
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Let P2 be the vector space of all polynomials of degree ≤ 2 with coefficients in R, and
S= {1 + 2x, 1 + 3x + 5x^2 , 4x + 5x^2 } .Is Span(S)= P2?

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