Problem

Given the function f(x)=x3−3x2−4x+12, find the zeros of the function and their multiplicities.

Answer

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Answer

Finally, set each factor equal to zero to find the zeros: x−3=0, x−2=0, and x+2=0. The solutions are x=3, x=2, and x=−2.

Steps

Step 1 ：First, we set the function equal to zero to solve for x: x3−3x2−4x+12=0.

Step 2 ：Next, we attempt to factor the function: f(x)=x3−3x2−4x+12=(x−3)(x−2)(x+2).

Step 3 ：Finally, set each factor equal to zero to find the zeros: x−3=0, x−2=0, and x+2=0. The solutions are x=3, x=2, and x=−2.

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