How do you factor the expression #x^2-x-42#?

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Answer 1 · 2018-03-22T10:51:50

#(x+6)(x-7)#

#x^2-x-42#

#=> x^2-7x+6x-42#

#=> x(x-7)+6(x-7)#

#=> (x+6)(x-7)#

Answer 2 · 2018-03-22T10:54:42

#(x+6)(x-7)#

The coefficient of #x^2# is #bb1#, so the factors will be of this form:

#(x +a)(x+b)#

We are looking for an #bba# and a #bb(b)# such that:

#axxb=-42#

#a+b=-1#

Possible factors for #a xx b =-42# are:

#-1 xx 42#

#1 xx 42#

#2xx-21#

#-2xx21#

#6xx-7#

#-6xx7#

#3xx-14#

#-3xx14#

The sum has to equal -1.

We can see that the only factors with a sum of #-1# is #6 and -7#.

#6+(-7)=-1#

These are the required values:

#(x+6)(x-7)#

Expanding:

#(x+6)(x-7)=x^2-x-42#

As required.

With practice you will quickly find the required values without having to list them all.