The polynomials $$\(\mathrm{f}(x)\)$$ and $$\(\mathrm{g}(x)\)$$ are defined by $$\[ \mathrm{f}(x)=4 x^{3}+a x^{2}+8 x+15 \quad \text { and } \quad \mathrm{g}(x)=x^{2}+b x+18 \]$$ where $$\(a\)$$ and $$\(b\)$$ are constants. Given that the remainder is 40 when $$\(\mathrm{g}(x)\)$$ is divided by $$\((x-2)\)$$, find the value of $$\(b\)$$. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

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