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

2 Answers
Jim G.
Jul 5, 2018

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

Explanation:

#"the factors of "-42" which sum to "-1#
#"are "-7" and "+6#

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

Nam D.
Jul 5, 2018

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

Explanation:

Given: #x^2-x-42#.

With some #color(blue)(bb(magic))#, notice how it equals:

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

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

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

The #color(blue)(bb(magic))# is that you pick two numbers, say #a# and #b#, whose sum equals the coefficient of the middle term and whose product equals the last terms.

In other words, we get:

#ab=-42#

#a+b=-1#

Clearly, #-7# and #6# are the numbers.

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