We want to find a polynomial of degree 3 with the given roots and that meets the given boundary condition.
We will find the polynomial:
f(x) = -3*(x + 3)*(x + 1)*(x - 4)
We know that for a polynomial of degree N with roots {x₁, ..., xₙ} and a leading coefficient a, it can be written as:
p(x) = a*(x - x₁)*...*(x - xₙ)
Now we know that we have a polynomial of degree 3 and that the roots are: {-3, -1, 4}
Then we can write:
f(x) = a*(x - (-3))*(x - (-1))*(x - 4)
f(x) = a*(x + 3)*(x + 1)*(x - 4)
Now we also know that:
f(-2) = -18
We can use this to find the leading coefficient.
Then we can write:
f(-2) = -18 = a*(-2 + 3)*(-2 + 1)*(-2 - 4) = a*6
-18/6 = a = -3
Then our polynomial is:
f(x) = -3*(x + 3)*(x + 1)*(x - 4)
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https://brainly.com/question/13053190
