Use synthetic division to divide 2x^4-x-5x-6 by x-4. Then choose the
coefficient of the x^2 term.
a. 8
b. 31
c. 7
d. 23
e. none of these

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Request for Question Clarification by livioflores-ga on 08 Jan 2005 04:08 PST

Is this 2x^4-x-5x-6 the correct expression or some power is missing?
(For example 2x^4-x^3-5x-6 or 2x^4-x^2-5x-6)

Thank you.

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Clarification of Question by haylo-ga on 08 Jan 2005 06:54 PST

The question was missing something, sorry!  It's 2x^4 - x^2 - 5x - 6
divided by x - 4.  Thanks in advance!

Hi!!


You want to divide 2x^4 - x^2 - 5x - 6 by x - 4 using synthetic division:

Write all the coeficients of the dividend and the 4 of (x-4) in a dividing box:

        2  0  -1  -5  -6   /__4


Now we can proceed:

        2   0   -1   -5   -6   /__4
          +   +     +    + 
            8   32   124  476
      _________________________

        2   8   31   119  470


The first four numbers are the coefficients of the quotient, and the
final number is the remainder.

We have:
(2x^4 - x^2 - 5x - 6) = (2x^3 + 8x^2 + 31x +119)*(x-4) + 470
  

The coefficient of the x^2 term is 8, so the correct answer is a.


For reference and further explanations visit:
"Synthetic Division by x - a":
http://www.themathpage.com/aPreCalc/synthetic-division.htm


I hope this helps you.

Best regards.
livioflores-ga