Answer:
x-intercepts are ...
- x = -2 (multiplicity 2)
- x = 3 (multiplicity 1)
Step-by-step explanation:
Indeed, x = -2 is an x-intercept of the polynomial ...
f(x) = x^3 +x^2 -8x -12
The other x-intercepts are -2 and +3, meaning that x = -2 is a zero with multiplicity 2.
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I like a graph for sorting this out. If you want to determine the other roots algebraically, you can factor (x +2) from f(x) to find the remaining quadratic factor to be (x^2 -x -6). Then the complete factorization of f(x) is ...
f(x) = (x +2)(x^2 -x -6) = (x +2)(x +2)(x -3)
f(x) = (x +2)^2(x -3)
The given x-intercept has multiplicity 2. The remaining x-intercept is x = 3.
