On dividing 3x²+x²+2x+5 by a polynomial …
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Sia ? 6 years, 4 months ago
The given polynomial is 3x3 + x2 + 2x + 5
According to Division Algorithm,
Dividend = Quotient x Divisor + Remainder
{tex}\Rightarrow{/tex} f(x) = {tex}q ( x ) \times g ( x ) + r ( x ){/tex}
{tex}\Rightarrow g ( x ) = \frac { f ( x ) - r( x ) } { g ( x ) }{/tex}
Here,
f(x) = 3x3 + x2 + 2x + 5
q(x) = 3x - 5
r(x) = 9x + 10
{tex}g ( x ) = \frac { \left( 3 x ^ { 3 } + x ^ { 2 } + 2 x + 5 \right) - ( 9 x + 10 ) } { ( 3 x - 5 ) } = \frac { 3 x ^ { 3 } + x ^ { 2 } - 7 x - 5 } { 3 x - 5 }{/tex}
{tex}\therefore{/tex} g(x) = x2 + 2x + 1.
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