Question

How do you factor the expression `x^2 – 11x + 24`?

Answer 1

`(x - 3)(x - 8)`

Explanation:

In factoring, we know that:

`(x + a)(x + b) = x^2 + (a+b)x + (a*b)`
such that `a` and `b` be any value.

Since the sign of 24 is positive, we know that `a` and `b` are either both positive or both negative. In this case, since we know that the sign of `11x` is negative, we can deduce that both `a` and `b` are both negative.

In order to find out what `a` and `b` are...

`a + b = -11`
`a*b = 24`

So now we know that our factors are `-3` and `-8`.
`(x - 3)(x - 8)`