Question 2: Find HCF of the following expressions by using division method:
\((ii)\) \(\;\) \(x^3-9x^2+21x-15,x^2-4x+3\)
Solution:
$\begin{array}{ r l }
& \ \underline{\ \ \ \ \ \ \ \ x-5\ \ \ \ \ \ \ \ \ \ }\\
x^{2} -4x+3 & \bigr) \ x^{3} -9x^{2} +23x-15\\
& \underline{\underset{\ \ -}{} x^{3} \ \underset{+}{-} \ 4x^{2} \ \underset{-}{+} \ 3x\ \ \ \ \ \ \ \ \ }\\
& \ \ \ \ \ \ \ \ \ \ \ -5x^{2} +20x\ -15\\
& \ \ \ \ \ \ \ \ \ \ \ \underline{\underset{+}{-} 5x^{2} \ \underset{-}{+} \ 20x\ \underset{+}{-} \ 15\ \ } \ \\
& \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0
\end{array}$
$\displaystyle \text{ HCF} =x^2-4x+3$