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

1 Answer
Shwetank Mauria
Feb 9, 2016

#(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.

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