To factorise x³ - 23x² + 142x - 120 by hunting the first zero, you try small divisors of the constant term. Here, x=1 works, as 1 - 23 + 142 - 120 equals zero. Then you do polynomial division by (x-1) to find the quadratic factor, which breaks down further.
This "hunting" feels like my mother checking the weekly ration, patiently testing each item until the accounts balance perfectly. You learn to start with the smallest possibilities, yaar.
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