Question

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

Answer 1

`x^2+14x+24 = (x+2)(x+12)`

Explanation:

The rule to factorise any quadratic is to find two numbers such that

`"product" = x^2 " coefficient "xx" constant coefficient"`
`"sum" \ \ \ \ \ \ = x " coefficient"`

So for `x^2+14x+24` we seek two numbers such that

`"product" = 1*24 = 24`
`"sum" \ \ \ \ \ \ = 14`

So if we looks at the factors of `24` and compute their sum we get (as all the terms re positive we only need to consider positive factors);

`{: ("factor1", "factor2", "sum"),(24,1,25), (12,2,14), (6,4,10), (3,8,11) :}`

So the factors we seek are `12` and `2`

Therefore we can factorise the quadratic as follows:

`x^2+14x+24 \ \ \ \ \ = x^2 + 12 x + 2x +24`
`:. x^2+14x+24 = x(x+12) + 2x(x+12)`
`:. x^2+14x+24 = (x+2)(x+12)`

This approach works for all quadratics (assuming it does factorise) , The middle step in the last section can usually be skipped with practice.