Question

Which polynomial should be subtracted from y³ + 2y² + 5y − 1 to get 2y² + 12?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{polynomial}\mathrm{to}\mathrm{be}\mathrm{subtracted}\mathrm{be}p\left(x\right). \\ \mathrm{Then}\left(y^3+2y^2+5y-1\right)-p\left(x\right)=\left(2y^2+12\right) \\ \Rightarrow p\left(x\right)=\left(y^3+2y^2+5y-1\right)-\left(2y^2+12\right) \\ =y^3+2y^2+5y-1-2y^2-12 \\ =y^3+2y^2-2y^2+5y-1-12 \\ =y^3+5y-13 \\ \therefore y^3+5y-13\mathrm{should}\mathrm{be}\mathrm{subtracted}\mathrm{from}{y}^3+2y^2+5y-1\mathrm{to}\mathrm{get}2y^2+12. \end{gathered}$$