Question

factorise x²+x-(p+1)(p+2)​

Answer 1

$\large\underline{\sf{Solution-}}$

Given expression is

$\rm :\longmapsto\: {x}^{2} + x - (p + 1)(p + 2)$

$\rm \:  =  \:  \: {x}^{2} + (2 - 1)x - (p + 1)(p + 2)$

$\rm \:  =  \:  \: {x}^{2} + (2 - 1 + p - p)x - (p + 1)(p + 2)$

$\rm \:  =  \:  \: {x}^{2} + (p + 2 - p - 1)x - (p + 1)(p + 2)$

$\rm \:  =  \:  \: {x}^{2} + (p + 2)x - (p + 1)x - (p + 1)(p + 2)$

$\rm \:  =  \:  \: {x} \bigg(x + (p + 2) \bigg) - (p + 1) \bigg(x + (p + 2) \bigg)$

$\rm \:  =  \:  \: (x + p + 2)(x - p - 1)$

Hence,

$\rm :\longmapsto\: \: {x}^{2} + x - (p + 1)(p + 2)=(x + p + 2)(x - p - 1)$