Step-by-step explanation
We must construct a polynomial with the following characteristics:
0. degree: 3,
,
1. zeros: x₁ = -3, x₂ = -1 and x₃ = 2,
,
2. passes through the point (3, 5).
The general form for this polynomial is:
Where a is a constant factor and x₁, x₂ and x₃ are the zeros of the polynomial.
Replacing the values of the zeros, we have:
Using the condition that the polynomial passes through (3, 5), we have:
Solving for a, we get a = 5/24. Replacing this value in the equation above, we get:
Answer