we are asked to determine the factor for the given expression. We can fill the given table in the following way:
What we have is the following:
On the top left square we have:
[tex]x\times x=x^2[/tex]
On the top right we have:
[tex]-12\times x=-12x[/tex]
On the bottom left we have:
[tex]-3\times x=-3x[/tex]
And in the bottom right we have:
[tex]-12\times-3=36[/tex]
Therefore, inside the square we have:
Adding all the terms in the squares we get:
[tex]x^2-12x-3x+36=x^2-15x+36[/tex]
Therefore, The last term in the sum is 36.
The factored form is the following:
[tex]x^2-15x+36=(x-12)(x-3)[/tex]
