solve this mathematics for me

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Divide:   -247x3 - 11x2 + 316x + 142


19x + 14

Oct 6th, 2015

Hello!

-247x^3 - 11x^2 + 316x + 142 / 19x + 14.

First, divide 247 by 19, it is 13. So -247x^3 = (19x + 14)*x^2*(-13) + 14*13*x^2 = (19x + 14)*x^2*(-13) + 182x^2.

So -247x^3 - 11x^2 + 316x + 142 = -13*(19x + 14)*x^2 + 182x^2 - 11x^2 + 316x + 142 =  -13*(19x + 14)*x^2 + 171x^2 + 316x + 142.

Now consider the remainder, 171x^2 + 316x + 142, and divide 171 by 19, it is 9.
Then 171x^2 + 316x + 142 = 9*x*(19x + 14) - 9x*14 + 316x + 142 = 9*x*(19x + 14) + 190x + 142.

And 190x + 142 = 10*(19x + 14) - 140 + 142 = 10*(19x + 14) + 2.

The answer: -247x^3 - 11x^2 + 316x + 142 = (19x + 14)*(-13x^2 + 9x + 10) + 2

Please ask if something is unclear.
Oct 6th, 2015

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