SOLUTION: “Synthetic Divison” Use synthetic division to find the quotient and remainder of the following: x^3+2x^2-3x+1 is divisible by x+1

Algebra ->  Divisibility and Prime Numbers -> SOLUTION: “Synthetic Divison” Use synthetic division to find the quotient and remainder of the following: x^3+2x^2-3x+1 is divisible by x+1      Log On


   

Question 1131336: “Synthetic Divison”
Use synthetic division to find the quotient and remainder of the following:
x^3+2x^2-3x+1 is divisible by x+1
Found 2 solutions by MathLover1, josgarithmetic:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E3%2B2x%5E2-3x%2B1%29%2F%28x%2B1+%29
Write down the coefficients of the polynomial. Put the zero from x%2B1=0 ( x=-1 ) at the left.

highlight%28-1%29 1 2 +-3 1
------------------------------

Bring down the leading coefficient to the bottom row.
highlight%28-1%29 1 2 +-3 1
------------------------------
------1
Multiply by the number on the left, and carry the result into the next column: -1%2A1=-1

highlight%28-1%29 1 2 +-3 1
.............-1
------------------------------
------1

Add down the column: 2%2B%28-1%29=1
highlight%28-1%29 1 2 +-3 1
............-1
------------------------------
------1 1
Multiply by the number on the left, and carry the result into the next column:+-1%2A1=-1

highlight%28-1%29 1 2 +-3 1
............-1 -1
------------------------------
------1 1
Add down the column: -3%2B%28-1%29=-4

highlight%28-1%29 1 2 +-3 1
............-1 -1
------------------------------
.......1 1 -4

Multiply by the number on the left, and carry the result into the next column:+-1%2A%28-4%29=4
highlight%28-1%29 1 2 +-3 1
...........-1 -1 4
------------------------------
......1 1 -4

Add down the column: 1%2B4=5
highlight%28-1%29 1 2 +-3 1
...........-1 -1 4
------------------------------
......1 1 -4 5

Bottom line represents the polynomial quotient %28x%5E2%2Bx-4%29 with a remainder of 5
so,
%28x%5E3%2B2x%5E2-3x%2B1%29%2F%28x%2B1+%29=x%5E2%2Bx-4%2B5%2F%28x%2B1%29

Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
Synthetic Division
as if checking -1 for root 

-1    |    1    2    -3    1
      |        -1   -1     4
      |_________________________
           1    1    -4    5

f%28-1%29=5

x%5E2%2Bx-4%2B5%2F%28x%2B1%29