How do you factor #x^2 - 7x + 12#?

1 Answer
Jul 23, 2016

Answer:

#(x-3)(x-4)#

Explanation:

We are looking for factors of 12 which ADD (because of + 12) up to 7.

The signs will be the same (because of + 12), they are both negative (because of -7).

The factors which satisfy both conditions are #-3 and -4.#

#-3 xx -4 = +12, and -3 + -4 = -7#

#(x-3)(x-4)#

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Let's look at the possible combinations of factors of #12#

#ul("subtract"color(white)(..................)12color(white)(..................)"add")#
#darrcolor(white)(...........................)darrcolor(white)(.....................)darr#

#11color(white)(.......................)1xx12color(white)(..................)13#
#4color(white)(...........................)2xx6color(white)(.....................)8#
#1color(white)(...........................)color(red)(3xx4)color(white)(.....................)color(red)(7)larr" "3 and 4# are the
#color(white)(.......................................................................)#factors we need.

In order to factorise easily you have to know the multiplication tables well. Without that it is a long slog with lots of trial and error!
Learn the tables!