How do you factor #x^2+3x-4=0#?

1 Answer
Aug 2, 2016

#(x-1)(x+4)#

Explanation:

In order to determine the factorised form of the given equation we must determine the factors of the #+3x+ and the #-4# coefficients:

For the #+3x# value:

The only factors of 3 (as it is a prime number) are #3# and #1#:

For the #-4# coefficient:

The factors of #-4# are:

#-4# and #1#
#4# and #-1#
#-2# and #2#
#2# and #-2#

If we consider that in the factorised form the sum of two factors of the #-4# term must equal #+3#, then we can determine that the required values are #-1# and #4# as these are the only values that when added form #+3#:

As a result, the factorised form of the given equation is:

#(x-1)(x+4)#