Question

How do you factor `p^2 + 12p + 32`?

Answer 1

If `(p^2+12p+32)`
`color(white)("XXXX")`has factors `(p+a)(p+b)`

then we need to find values `a` and `b` such that
`color(white)("XXXX")` `a+b = 12` and
`color(white)("XXXX")` `axxb= 32`

With a bit of consideration of the possible factors of `32`
we can come up with `(4,8)`

So
`color(white)("XXXX")` `p^2+12p+32 = (p+4)(p+8)`