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.Com
Question 174647:
answer:
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)   (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)   (Show Source): You can put this solution on YOUR website!
Edwin's solution:

answer: 


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:  or  

Edwin
RELATED QUESTIONS

x^3 + 2x^2 - 5x + 12/ x+4 answer:x^2-2x+3 need a full break down of how my text... (answered by Mathtut)
solve 2r^2 + 3r-1=0 answer: -3 + sqrt 17/4, -3-sqrt 17/4 need a full break down... (answered by yuendatlo)
18x^2 +9x + 1=0 answer: x= -1/3 or -1/6 need a full break down of how my text (answered by jim_thompson5910)
x^4 - x^3 - 9x^2 +14x - 4/ x^2 -3x + 1 answer:x^2 + 2x - 4 need a full break... (answered by Mathtut)
{{{ (t^2-1)/(t^2-4) }}} + {{{ (9t+9)/(4t+12) }}} * {{{ (2-t)/(t^2+2t-3) }}} The back... (answered by Alan3354,greenestamps,MathTherapy)
x^2 + 2x= 3/4=0 answer x= -3/2 or -1/2 need a full break down of how my book... (answered by Alan3354)
1=3x^2+ 2x answer x= -1 or 1/3 need a break down of how my text book got this... (answered by Mathtut)
1=3x^2 + 2x answer: x=-1 or 1/3 need a break down of how my text book got this... (answered by Mathtut)
x^2 + 5x+ 4=0 answer:x=-1 or -4 need a full break down of how my text book got... (answered by jim_thompson5910)