Let $S$ be the subspace of $P_{3}$ consisting of all polynomials of the form $a x^{2}+b x+2 a+3 b$. Find a basis for $S$.
Added by Vicenta W.
Step 1
First, we can rewrite the polynomial as follows: $$a x^{2}+b x+2 a+3 b = a(x^2 + 2) + b(x + 3)$$ Now, we can see that the polynomial is a linear combination of two polynomials: $x^2 + 2$ and $x + 3$. Show more…
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