Long Division

Algebra 2 Tutorial

Long Division

Intro

There are two ways to do division with polynomials, which are long(polynomial) division and synthetic division. In these two sample problems, this would only be done through long division. Synthetic division is the shortcut, but it only works with linear factors. You have to find the solution for x, so it can be used in synthetic division.

Sample Problem

1. What is x^2-7x+12 divided by x-3?
2. What is x^3-8x^2-5x+3 divided by x-2?

Solution

    x-4
   ___________
x-3)x^2-7x+12
  -(x^2-3x)
  _____________
        -4x+12
      -(-4x+12)
    _____________
           0

    x^2-6x-17- 31/x-2
   ________________
x-2)x^3-8x^2-5x+3
  -(x^3-2x^2)
 _________________
       -6x^2-5x
   - (-6x^2+12x)
 __________________
             -17x+3
           -(-17x+34)
        ______________
                  -31
 


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