Question

How do you factor the expression `x^2-10x+24`?

Answer 1

`(x-6)(x-4)`

Explanation:

We attempt to generate factors in the form:
`color(white)("XXX")(x+a)(x+b)`

Since the constant term: `+24` is positive
we know that `a` and `b` have the same sign.

Since the middle term: `(-10x)` is negative
we know that `a` and `b` are negative.

All that remains is to find factors of `24`
that add up to `10`

Factors of `24`
`color(white)("XXX"){(1,24), (2,12), (3,8), (4,6)}`

Only the factors `(4,6)` add up to `10`