Question

How do you factor the trinomial `x^2 - 5x + 4`?

Answer 1

`(x-1)*(x-4)`

Explanation:

Let the equation be `a*x^2+b*x+c`. To factorize multiplication of a and c i.e. ac so that sum of factors, if ac is positive (and difference if ac is negative) is equal to b. Now split b into these two components and factorization will be easy.

For example in above case `a=1`, `b=-5` and `c=4`.

Hence `ac=4` and so split b in 1 and 4 as given below.

`x^2-5*x+4`

= `x^2-4*x-1*x+4`

= `x(x-4)-1(x-4)`

= `(x-1)*(x-4)`

In case ac can not be factorized into factors, whose sum / difference (whatever is applicable) is b than the factors may be irrational and/or complex.