Answer :
To factor a expression of the form:
[tex]x^2+Bx+C[/tex]we need to find two integers a and b that fulfills the following conditions:
[tex]\begin{gathered} ab=C \\ a+b=B \end{gathered}[/tex]In that way we write the original expression as:
[tex]x^2+Bx+C=x^2+ax+bx+C[/tex]and then we facto by grouping.
Let's make the example to understand this better.
[tex]p^2-12p+20[/tex]In this case B=-12 and C=20. We need to find two numbers that fulfills:
[tex]\begin{gathered} ab=20 \\ a+b=-12 \end{gathered}[/tex]We see that the numbers a=-2 and b=-10, fulfill this conditions. Then we write the expression as:
[tex]p^2-12p+20=p^2-2p-10p+20[/tex]and now we factor the first pair and second pair of terms by common factors:
[tex]\begin{gathered} p^2-12p+20=p^2-2p-10p+20 \\ =p(p-2)-10(p-2) \\ =(p-2)(p-10) \end{gathered}[/tex]Therefore:
[tex]p^2-12p+20=(p-2)(p-10)[/tex]