Question 2: Find the square root of the following polynomials by division method:
\((ii)\) \(\; \) \(121x^4-198x^3-183x^2+216x+144\)
Solution:
$\small
\begin{array}{ r l }
& \ \ \ \ \ \ \ \underline{\ \ \ \ \ \ 11x^{2} -9x-12\ \ \ \ \ \ \ \ }\\
& 11x^{2}\bigr) \ \ \cancel{121x^{4}} -198x^{3} -183x^{2} +216x+144\\
& \ \ \ \ \ \ \ \ \ \ \underline{\underset{-}{+}\cancel{121x^{4}} \ \ \ \ \ \ \ \ \ \ }\\
& 22x^{2} -9x\ \overline{) -\cancel{198x^{3}} -183x^{2} +216x+144}\\
& \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \underline{\ \underset{+}{-} \ \cancel{198x^{3}} \ \underset{-}{+} \ 81x^{2} \ \ \ \ } \ \\
& 22x^{2} -18x-12\ \overline{) -264x^{2} +216x+144}\\
& \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \underline{\ \ \ \ \underset{+}{-} 264x^{2} \ \ \underset{-}{+} 216x\ \underset{-}{+} \ 144\ }\\
& \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0
\end{array}$
So, $\displaystyle \text{Square Root } =\pm \left( 11x^{2} -9x-12\right)$