on dividing x cube minus 3 …
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Sia ? 6 years, 6 months ago
we have, Dividend = divisor × quotient + remainder
{tex}\Rightarrow{/tex}{tex}{/tex}{tex}f(x)\;=\;g(x).\;q(x)\;+\;r(x){/tex}
{tex}\Rightarrow\ x^3\;–\;3x^2\;+\;x\;+\;2\;=\;\;g(x)\;\times\;(x\;–\;2)\;–\;2x\;+\;4{/tex}
{tex}\Rightarrow\ x^{3\;}–\;3x^2\;+\;x\;+\;2\;+\;2x\;–\;4\;=\;g(x)\;\times\;(x\;–\;2){/tex}
{tex}\Rightarrow{/tex} {tex}x^3\;–\;3x^2\;+3\;x\;\;\;–\;2\;=\;g(x)\;\times\;(x\;–\;2){/tex}
{tex} \Rightarrow\ g ( x ) = \frac { x ^ { 3 } - 3 x ^ { 2 } + 3 x - 2 } { ( x - 2 ) }{/tex}
{tex}\Rightarrow\ g ( x ) = \left( x ^ { 3 } - 3 x ^ { 2 } + 3 x - 2 \right) \div ( x - 2 ){/tex}
g(x) = x2 – x + 1
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