# Long division of polynomials

• Dec 9th 2007, 05:25 PM
MathMack
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!
• Dec 10th 2007, 01:41 AM
earboth
Quote:

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
• Dec 10th 2007, 02:04 AM
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.

Attachment 4665

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