How do you factor #f(x)= x^2-614x-125712#?

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Answer 1 · 2016-07-29T05:48:20

#f(x)=(x-776)(x+162)#

The difference of squares identity can be written:

#a^2-b^2 = (a-b)(a+b)#

We use this later with #a=(x-307)# and #b=469#

#color(white)()#
Complete the square:

#614/2 = 307#

#307^2 = 94249#

#94249+125712 = 219961 = 469^2#

So:

#f(x) = x^2-614x-125712#

#=(x-307)^2-94249-125712#

#=(x-307)^2-469^2#

#=((x-307)-469)((x-307)+469)#

#=(x-776)(x+162)#