there is only one cubic which passes through all four of those points:
p(x) = x^3-3x^2-4x+5
no need to approximate p(1), since you can see that it is -1.
As for p(x) = 0, you'll have to approximate that, using a graph, or some other numeric tool you have studied, such as: ??
Find a polynomial p of degree 3 so that
p(4) = 5,
p(−1) = 5,
p(−3) = −37,
p(2) = −7,
then use your polynomial to approximate p(1).
p(x) = 0
p(1) = 0
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