Algebra help needed about synthetic division

Anonymous
timer Asked: Nov 1st, 2015
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Question Description

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

Tutor Answer

alancheng
School: Boston College

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
2-810-12



2*40*41*44*4


20144

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.

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Anonymous
awesome work thanks

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