Question #9c7c9

1 Answer
Alan P.
Oct 3, 2017

#x^2-14x+49=color(blue)((x-7)(x-7)# or #color(blue)((x-7)^2)#

Explanation:

I assumed the #x^*# was meant to be #x^2#

In general #(x+a)(x+b)=x^2+(a+b)x+ab#

In this case
#color(white)("XXX")a+b=-14#
and
#color(white)("XXX")ab=49#

If we consider integer factors (in the hopes of "getting lucky") for #49# we find only
#1xx49#,
#49xx1#,
#7xx7# and
#(-7)xx(-7)#

Comparing these possibilities with the requirement that #a+b=-14#
we find #a=-7# and #b=-7#
So
#(x+a)(x+b)# becomes #(x-7)(x-7)#

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