How can polynomial functions be written when given the zeros? can anybody give me a simple answer no examples

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How can polynomial functions be written when given the zeros? can anybody give me a simple answer no examples

Mathematics
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given the zeros a , b and c we can write P(x) = (x - a)(x - b)(x - c)
there will be infinite polynomials with those roots.
you can the expand this to obtain standard form

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Other answers:

\(p(x)=k(x-a)(x-b)(x-c)\)
and of course, if there were more roots there would be more binomial factors...
ah yes i missed the constant k
can you put that all together please CX it is confusing me CX lol
what part don't you understand - why the k had to be added ?
k can be any constant:- 2 , 6, 0.25 whatever
and following on from zzrock's post you can have more than 3 roots - for each root there will be another binomial for 4 roots we would have p(x) = k(x-a)(x-b)(x-c)(x-d)

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