Question 2: Find HCF of the following expressions by using division method:
\((i)\) \(\;\) \( 27x^3+9x^2-3x-9,3x-2\)
Note: The question given in the book is incorrect. The correct form of the question should be: \( 27x^3+9x^2-3x-10,3x-2\)
Solution:
$\begin{array}{ r l }
& \ \underline{\ \ \ \ \ \ \ \ 9x^{2} +9x+5\ \ \ \ \ }\\
3x-2 & \bigr) \ \ 27x^{3} +9x^{2} -3x-10\\
& \underline{\underset{\ \ -}{} 27x^{3} \ \underset{+}{-} 18x^{2} \ \ \ \ \ \ \ \ \ }\\
& \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 27x^{2} -3x-10\\
& \ \ \ \ \ \ \ \ \ \ \ \ \ \ \underline{\underset{-}{} 27x^{2}\underset{+}{-} 18x\ \ \ \ } \ \\
& \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 15x-10\\
& \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \underline{\underset{-}{} 15x\ \underset{+}{-} \ 10}\\
& \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0
\end{array}$
$\displaystyle \text{ HCF} =3x-2$