x2+9x+20
s2-100
t2-3t-28
36m2-121
How do you factor
The first and third have a leading coefficient of 1. So you know that the first terms have to be
$\displaystyle x^2 + 9x + 20 = ({\color{red}x}\;+\;?)({\color{red}x}\;+\;?)$
To fill in the last terms, ask yourself, what are the factors of 20 whose sum is 9? It's +4 and +5, so fill them in:
$\displaystyle x^2 + 9x + 20 = (x\;+\;{\color{red}4})(x\;+\;{\color{red}5})$
The second and fourth are one of the special patterns that you should memorize -- these involve difference of two squares. The pattern is
$\displaystyle a^2 - b^2 = (a + b)(a - b)$
a would correspond to s, and b would correspond to 10:
$\displaystyle s^2 - 100 = s^2 - 10^2 = (s\;+\;10)(s\;-\;10)$
I'll let you try the other two.
01