How do you FOIL x^2+111x-104000 ?

1 Answer
George C.
Jan 20, 2018

x^2+111x-104000

= (x+111/2-sqrt(428321)/2)(x+111/2+sqrt(428321)/2)

Explanation:

I think you are wanting to factor x^2+111x-104000

We find:

4(x^2+111x-104000)

= 4x^2+444x-416000

= (2x)^2+2(2x)(111)+111^2-428321

= (2x+111)^2-(sqrt(428321))^2

= ((2x+111)-sqrt(428321))((2x+111)+sqrt(428321))

= (2x+111-sqrt(428321))(2x+111+sqrt(428321))

So:

x^2+111x-104000

= 1/4(2x+111-sqrt(428321))(2x+111+sqrt(428321))

= (x+111/2-sqrt(428321)/2)(x+111/2+sqrt(428321)/2)

Note that 428321 = 107 * 4003 has no square factors, so sqrt(428321) is in simplest form.

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