The figure below shows a shaded rectangle inside a large rectangle:
2 answers:
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If a polynomial "contains", in a multiplicative sense, a factor , then the polynomial has a zero at
.
So, you polynomial must contain at least the following:
If you multiply them all, you get
Now, if you want the polynomial to be zero only and exactly at the four points you've given, you can choose every polynomial that is a multiple (numerically speaking) of this one. For example, you can multiply it by 2, 3, or -14.
If you want the polynomial to be zero at least at the four points you've given, you can multiply the given polynomial by every other function.