question_answer

Check whether polynomial \[x-1\] is a factor of the polynomial \[{{x}^{3}}-8{{x}^{2}}+19x-12\]. Verify by division algorithm.

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.