if the polynomial x⁴+2x^​3+8x²+12x+18 is divided by another polynomial (x²+5), the remainder comes out to be (px+q). find the values of p and q.

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{We} \mathrm{have} \\ \frac{{\mathrm{x}}^4+2{\mathrm{x}}^3+8{\mathrm{x}}^2+12\mathrm{x}+18}{{\mathrm{x}}^2+5} \end{gathered}$$

$$\begin{gathered} \mathrm{Here} \mathrm{remainder} \mathrm{is} 2\mathrm{x}-9. \\ \mathrm{On} \mathrm{comparing} \mathrm{ot} \mathrm{with} \mathrm{px}+\mathrm{q}, \mathrm{we} \mathrm{get}, \\ \boxed{\mathbf{p}\mathbf{=}\mathbf{2}\mathbf{ }\mathbf{and}\mathbf{ }\mathbf{q}\mathbf{=}\mathbf{-}\mathbf{9}} \end{gathered}$$


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