Find a polynomial p of degree 3 so that

Question

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

Answer 1

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: ??