SOLUTION: {{{(t^3-19t +9)/(t-4)}}} answer: {{{ matrix(1,3,t^2+4t-3, "",r=-3) }}} need a full break down of how my text book got that answer can go as far as getting t^2 please help

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: {{{(t^3-19t +9)/(t-4)}}} answer: {{{ matrix(1,3,t^2+4t-3, "",r=-3) }}} need a full break down of how my text book got that answer can go as far as getting t^2 please help       Log On


   



Question 174647: %28t%5E3-19t+%2B9%29%2F%28t-4%29
answer: +matrix%281%2C3%2Ct%5E2%2B4t-3%2C+%22%22%2Cr=-3%29+
need a full break down of how my text book got that answer can go as far as getting t^2 please help

Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
t^3-19t +9/t-4=
answer:t^2 + 4t-3 r-3
--------------
Use synthetic division:
4)....1....0....-19....9
.......1....4.....-3...|..-3
Quotient: x^2 + 4x - 3
Remainder: -3
===========================
Cheers,
Stan H.

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Edwin's solution:
%28t%5E3-19t+%2B9%29%2F%28t-4%29
answer: +matrix%281%2C3%2Ct%5E2%2B4t-3%2C+%22%22%2Cr=-3%29+


By inserting the term 0t2 and using long division
or synthetic division.

Do you understand long division or synthetic division? 
If not post again asking how we get the following:

              t2 +  4t -  3 
      --------------------- 
t - 4 ) t3 - 0t2 - 19t +  9
        t3 - 4t2
        --------
             4t2 - 19t
             4t2 - 16t
             ---------
                    3t +  9
                    3t + 12 
                   --------
                         -3

Answer: t2 + 4t - 3  r=-3

Or by synthetic division:

4 | 1  0  -19   9
  |    4   16 -12  
  ---------------
    1  4   -3  -3   

Answer: t2 + 4t - 3  r=-3

Or if you know to put the remainder over the dividend:

Answer: t%5E2+%2B+4t+-+3+%2B+%28-3%29%2F%28t-4%29 or t%5E2+%2B+4t+-+3+-+3%2F%28t-4%29 

Edwin