 # Algebra help needed about synthetic division Anonymous
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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

alancheng
School: Boston College   You want to divide the polynomial (2*x^4 - 8*x^3 + 1*x^2 + 0*x - 12)  by  binomial (x-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.

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