Question 124378
Can someone please help me with this problem?
The last line of synthetic division for (2x^4-5x^3+7x^2-3x+1)/(x-3) gives coefficients for the quotient of 2,1,8,21.
Is this true or false?
I thought the answer was false. Am I right please help!!!
<pre><b>
We'll have to do it and see.  There's no other way:

3|2 -5  7 -3  1
 |<u>   6  3 30 81</u>
  2  1 10 27 82

What that tells us is that the coefficients for
the quotient are 2, 1, 10, and 27 and that the remainder
is 82.  That means that the quotient is

{{{2x^3 + 1x^2 + 10x + 27 + 82/(x-3)}}}

or, erasing the 1 coefficient on {{{x^2}}}:

{{{2x^3 + x^2 + 10x + 27 + 82/(x-3)}}}

So the answer is indeed false, but getting it right simply 
by lucky guessing would most likely not be acceptable to your 
teacher.

Edwin</pre>