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 $b=469$

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Complete the square:

$614/2 = 307$

$307^2 = 94249$

$94249+125712 = 219961 = 469^2$

So:

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

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

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

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

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

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