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Answer:
f(x) = 3x³ +6x² -3x -6
Step-by-step explanation:
Each x-intercept (x=p) gives rise to a factor (x-p), so the factored form of the function is ...
f(x) = a(x -(-2))(x -(-1))(x -1)
The value of 'a' is chosen to make the y-intercept match that shown. The function just written has ...
f(0) = -6 = a(2)(1)(-1)
-6 = -2a
a = 3 . . . . . divide by -2
So, the function in factored form is ...
f(x) = 3(x +2)(x +1)(x -1)
Expanded, this is ...
f(x) = 3x³ +6x² -3x -6
