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Sagot :
Every polynomial can be written in the form:
[tex]f(x)=(x-a_1)(x-a_2)\ldots_{}[/tex]The a_1, a_2.... are the roots of the polynomial, meaning that f(a_1) = f(a_2) = ... = 0. This happens wen the graph of the polynomial intersects or tangency the x-axis. Whe it only tangecy the x-axis, it means that you have two of the root.
In this case, we have the polynomial tangency the x-axis in x = -2 and intersect the x-axis in x = 3. This means that the polynomial has roots -2, -2 (again) and 3. So:
[tex]\begin{gathered} f(x)=(x-(-2))(x-(-2))(x-3) \\ f(x)=(x+2)(x+2)(x-2) \\ f(x)=(x+2)^2(x-3) \end{gathered}[/tex]Since the order doesn't metter, we can right in this way:
[tex]f(x)=(x-3)(x+2)^2[/tex]Which corresponds to alternative D.
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