We have been given a polynomial and we are asked to factor our polynomial by double grouping.
[tex]x^{2} +2x-3x-6[/tex]
First of all we will group terms with common factors. We can see that [tex]x^{2}[/tex] and 2x have a common factor x. Common factor of -3x and -6 is -3.
[tex]x^{2} +2x-3x-6[/tex]
[tex](x^{2} +2x)+(-3x-6)[/tex]
Now we will factor out Greatest Common Factor from each group.
[tex]x(x+2)-3(x+2)[/tex]
After factoring out GCF from each group we got (x+2) as our common binomial. Now we will write our polynomial as a product of two binomials as:
[tex](x+2)(x-3)[/tex]
Therefore, our polynomial as a product of two binomials will be [tex](x+2)(x-3)[/tex].
