Question

factorize (x^2-2x^2) -11(x^2-2x)+24​

Answer 1

Answer:(x+1)(x+2)(x-3)(x-4)

Steps:

$p(x)= (x^{2} -2x)^{2} -11(x^{2} -2x) +24\\Let (x^{2} -2x)=y\\p(x)= y^{2} -11y+24\\      =  y^2-3y-8y+24\\=y(y-3)-8(y-3)\\=(y-3)(y-8)\\Substituting: y=(x^{2} -2x)\\\\p(x) = (x^{2} -2x-3)(x^{2} -2x-8)\\=(x^{2} -3x+x-3)(x^{2} -4x+2x-8)\\=[(x-3)(x+1)][(x-4)(x+2)]\\=(x+1)(x+2)(x-3)(x-4)$