Using remainder theorem, find the remainder when $f( x)$ is divided by $g( x)$:$f( x)=4 x^{3}-12 x^{2}+11 x-3,\ g( x)=x+\frac{1}{2}$.
Given: $f( x)=4 x^{3}-12 x^{2}+11 x-3$ and $g( x)=x+\frac{1}{2}$.
To do: To find the remainder when $f( x)$ is divided by $g( x)$.
Solution:
As given, $f( x)=4 x^{3}-12 x^{2}+11 x-3$ and $g( x)=x+\frac{1}{2}$.
On dividing $f( x)$ by $g( x)$:
Thus, when we divide $f( x)$ by $g( x)$, the remainder is $-12$.
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