Question

Is it possible to factor `y=x^2 +8x+15`? If so, what are the factors?

Answer 1

`y=x^2+8x+15= color(green)((x+3)(x+5))`

Explanation:

Since `(x+a)(x+b) = x^2+(a+b)x+ab`

we need to find two numbers `a` and `b`
such that
`color(white)("XXX")a+b=8`
and
`color(white)("XXX")ab=15`

Checking factors of `15` we quickly come up with `3` and `5` which sum to `8`