##### Algebra help needed about synthetic division

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Use synthetic division to determine the quotient Q(x) and the constant remainder R obtained when the first polynomial F(x) is divided by the binomial x-k.

2x^4 - 8x^3 + x^2 - 12  , x-4

Nov 1st, 2015

Thank you for the opportunity to help you with your question!

You want to divide the polynomial (2*x^4 - 8*x^3 + 1*x^2 + 0*x - 12)  by  binomial (x-4)

Here, your k = 4

Take the coefficients of the polynomial and start with the highest power. :  2 ,  -8,  1,  0,  -12

 4 2 -8 1 0 -12 2*4 0*4 1*4 4*4 2 0 1 4 4

From the synthetic division process in this table, we get a remainder of 4

And our Quotient  Q(x) =  2*x^3 + 0*x^2 + 1*x + 4    ;  R = 4

Answer  Simplify Q(x)  as  Q(x) = 2x^3 + x + 4;   R = 4

The coefficients of  Q(x) were in the last row of the table, excluding the last column.

Please let me know if you need any clarification. I'm always happy to answer your questions.
Nov 1st, 2015

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Nov 1st, 2015
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Nov 1st, 2015
Oct 17th, 2017
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