How do you factor the trinomial x^2 - 14x + 24?

1 Answer
Feb 27, 2016

The trinomial x^2-14x+24 can be factored as (x-2)(x-12).

Explanation:

Approach 1
Since both -14 and 24 are relatively small and easy numbers. We can just look for two numbers a,b that satisfy the following two equations:

ab=24
a+b=-(-14)=14.

After some experimentation, we arrive at our answer.

Approach 2
For quadratic equations in general, it often makes sense to simply go straight to the quadratic formula to solve for x directly.

It gives you x=7+-5. It is trivial to figure out the factorization from here.

Approach 3

We use

alpha + beta = -b/a
alpha * beta = c/a

In general we can express an equation as

(x-alpha)(x-beta)

so
14 = alpha + beta
24 = alphabeta

Now you can solve these 2 equation for alpha and beta

But on close inspection we find

alpha = 12, beta = 2

So the above equation is

(x-12 )(x-2)