Question # 01: Find HCF by factorization method:
\((vi)\) \(\; \) \(x^2+15x+56,x^2+5x-24,x^2+8x\)
Solution:
$\displaystyle x^{2} +15x+56=x^{2} +7x+8x+56$
$\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =x( x+7) +8( x+7)$
$\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =( x+7)( x+8)$
$\displaystyle x^{2} +5x-24=x^{2} +8x-3x-24$
$\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =x( x+8) -3( x+8)$
$\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =( x+8)( x-3)$
$\displaystyle x^{2} +8x=x( x+8)$
$\displaystyle \text{HCF} =x+8$