Construct a degree $n$ polynomial with roots $a_1, a_2, a_3, \ldots, a_n$

Question

We have the numbers: $a_1, a_2, a_3, \ldots, a_n$

Show that there is a polynomial $P(x)$ of degree $n$ such that $a_1, a_2, a_3, \ldots, a_n$ are roots of $P(x)$

Answer 1

HINT:

1. $b$ is said to be a root of a polynomial $f(x)=x-b$.
2. $a,b$ are said to be roots of a polynomial $f(x)=(x-a)(x-b)$.

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