Question Number 11023 by ABD last updated on 07/Mar/17
$$\left({x}^{\mathrm{3}} +\mathrm{6}\right)×{P}\left({x}\right)+\mathrm{6}{x}={ax}^{\mathrm{3}} +\mathrm{2}{ax}+{b}+\mathrm{3} \\ $$$$\Rightarrow{b}=? \\ $$
Answered by mrW1 last updated on 07/Mar/17
$$\left({x}^{\mathrm{3}} +\mathrm{6}\right)×{P}\left({x}\right)+\mathrm{6}{x}={ax}^{\mathrm{3}} +\mathrm{2}{ax}+{b}+\mathrm{3} \\ $$$${P}\left({x}\right){x}^{\mathrm{3}} +\mathrm{6}×{P}\left({x}\right)+\mathrm{6}{x}={ax}^{\mathrm{3}} +\mathrm{2}{ax}+{b}+\mathrm{3} \\ $$$$\Rightarrow{P}\left({x}\right)={a} \\ $$$$\Rightarrow\mathrm{6}=\mathrm{2}{a}\:\Rightarrow{a}=\mathrm{3} \\ $$$$\Rightarrow\mathrm{6}×{P}\left({x}\right)={b}+\mathrm{3}\:\Rightarrow{b}=\mathrm{6}×\mathrm{3}−\mathrm{3}=\mathrm{15} \\ $$