# Thread: Long division of polynomials

1. ## Long division of polynomials

1.)3x^2 + 2x+1 divided by X+2

2.) 5t-3 divided by t-2

3.) 6x^4 + 8x^2 -4 divided by 2x+4

any help is appreciated. Thanks everyone, you ROCK!

2. Originally Posted by MathMack
1.)3x^2 + 2x+1 divided by X+2

2.) 5t-3 divided by t-2

3.) 6x^4 + 8x^2 -4 divided by 2x+4

any help is appreciated. Thanks everyone, you ROCK!
Hello,
Code:
  (3x^2 + 2x + 1) / (x + 2) = 3x - 4 + 9/(x+2)
-(3x^2 + 6x)
----------------
-4x + 1
-(-4x - 8)
------------
9
Code:
   (5t - 3) / (t - 2) = 5 + 7/(t+2)
-(5t -10)
-----------
7
Code:
   (6x^4 +       8x^2         - 4) / (2x + 4) = 3x^3 - 6x^2 + 16x - 32 + 124/(2x + 4)
-(6x^4 + 12x^3)
-------------------
-12x^3 + 8x^2
-(-12x^3 - 24x^2)
--------------------
32x^2
-(32x^2 + 64x)
------------------
-64x - 4
-(-64x -128)
---------------
124

3. Edit: Sorry, didn't see Earboth's much neater post. Please ignore this.

1. Write the polynomials out as shown and make sure that they are in descending order of the powers.

2. divide the first term of the dividend by the first term of the divisor and write it above the line as shown.

3. Multiply this number by the divisor and write it underneath the dividend, keeping the same powers in the same columns

4. subtract the thingy under the dividend from the dividend.

5&6. repeat, using the thingy as the new dividend each time until it is a constant.

Then you have
$\displaystyle \frac {3x^2+2x+1}{x+2}$ = $\displaystyle 3x-4+\frac {9}{x+2}$