Alg3.6.4

From Exampleproblems

t Solve for $x: x^2-x-2=0\,$

Multiplying the coefficient of $x^2\,$ and the constant gives $-2\,$ The different factors for $35\,$ are $(2,-1)(-2,1)\,$ The combination which suits the coefficient of $-12\,$ is $(-2,1)\,$ Now splitting the $x\,$ coefficient,the equation looks like $x^2-2x+x-2=0\,$

Taking out the common in the first two and the last two terms $x(x-2)+1(x-2)=0\,$

Taking out the common terms in the above $(x-2)(x+1)=0\,$

Final solution is $(x-2)=0\,$ or $(x+1)=0\,$

$x=2\,$ or $x=-1\,$