Answer:
Let \[P(x)={{x}^{3}}-8{{x}^{2}}+19x-12\] Put \[x=1\], \[P(1)={{(1)}^{3}}-8{{(1)}^{2}}+19(1)-12\] \[=1-8+19-12\] \[=20-20\] \[=0\] \[\therefore \,\,(x-1)\] is a factor of \[P(x)\]. Verification: Since remainder \[=0\]. \[(x-1)\] is a factor of \[P(x)\]. Hence Verified.
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