= Solution
\b[The odd-power family is also dense on $[1,2]$.] It is $B=tA$, where $A$ is the even-power family in part (i). Multiplication by $t$ is an invertible bounded <linear map> on $C([1,2])$, with inverse division by $t$, since $t\geq1$.
For an explicit approximation, take any $f\in C([1,2])$ and $\epsilon>0$. The quotient $f(t)/t$ is continuous, so part (i) gives an even <polynomial> $a$ with $\|a-f/t\|_\infty<\epsilon/2$. Then $ta$ belongs to the odd-power family and
$$
\boxed{\|ta-f\|_\infty\leq2\|a-f/t\|_\infty<\epsilon.}
$$
Although this family is not a <subalgebra> and does not contain the constant function exactly, it can approximate every <continuous function>, including constants. This proves <even and odd polynomial density on a positive interval> without incorrectly applying the unital algebra theorem directly to the odd family.
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