diving polynomials

• Nov 6th 2008, 06:09 PM
Ace
diving polynomials
all i need is the division. PLEASE DO NOT SIMPLIFY ALL THE WAY!
example: (4x^2+2x)/2x = 2x+1

so

2. (4ab-2b) / -2b
3. (12rst-6rs^2t) / 3rs
4. 4y^3 - 2y^2 + 6y / (-2y)
5. (-18r^5t^2 + 12r^3t + 3rt) / 6rt
6. (21k^6l^4 + 14k^3l^3 - 7k^2l^2) / 7kl

please show work/explain so that i may learn!!! thankyou!!!
• Nov 7th 2008, 04:09 AM
earboth
Quote:

Originally Posted by Ace
all i need is the division. PLEASE DO NOT SIMPLIFY ALL THE WAY!
example: (4x^2+2x)/2x = 2x+1

so

2. (4ab-2b) / -2b
3. (12rst-6rs^2t) / 3rs
4. 4y^3 - 2y^2 + 6y / (-2y)
5. (-18r^5t^2 + 12r^3t + 3rt) / 6rt
6. (21k^6l^4 + 14k^3l^3 - 7k^2l^2) / 7kl

please show work/explain so that i may learn!!! thankyou!!!

With all your problems it is possible to factor out a greatest common factor which will be canceled with the denominator.

to #5.:

$\displaystyle \dfrac{-18r^5t^2 + 12r^3t + 3rt}{6rt}=\dfrac{3rt(-6r^4t + 4r^2 +1) }{3rt \cdot 2}$ Now cancel the common factors.
• Nov 7th 2008, 09:12 AM
Soroban
Hello, Ace!

A slightly different view . . .

Make separate fractions and reduce.

Quote:

$\displaystyle 1)\;\;\frac{4x^2+2x}{2x}$

We have: .$\displaystyle \frac{4x^2}{2x} + \frac{2x}{2x} \;=\;2x+1$

Quote:

$\displaystyle 2)\;\;\frac{4ab-2b}{\text{-}2b}$

We have: .$\displaystyle \frac{4ab}{\text{-}2b} - \frac{2b}{\text{-}2b} \;=\;-2a + 1$

Quote:

$\displaystyle 3)\;\; \frac{12rst-6rs^2t}{3rs}$

We have: .$\displaystyle \frac{12rst}{3rs} - \frac{6rs^2t}{3rs} \;=\;4t - 2st$

Quote:

$\displaystyle 4)\;\;\frac{4y^3 - 2y^2 + 6y}{\text{-}2y}$

We have: .$\displaystyle \frac{4y^3}{\text{-}2y} - \frac{2y^2}{\text{-}2y} + \frac{6y}{\text{-}2y} \;=\;-2y^2 + y - 3$

Quote:

$\displaystyle 5)\;\;\frac{\text{-}18r^5t^2 + 12r^3t + 3rt}{6rt}$

We have: .$\displaystyle \frac{\text{-}18r^5t^2}{6rt} + \frac{12r^3t}{6rt} + \frac{3rt}{6rt} \;=\;-3r^4t + 2r^2 + \tfrac{1}{2}$

Quote:

$\displaystyle 6)\;\;\frac{21k^6l^4 + 14k^3l^3 - 7k^2l^2}{7kl}$

We have: .$\displaystyle \frac{21k^6l^4}{7kl} + \frac{14k^3l^3}{7kl} - \frac{7k^2l^2}{7kl} \;=\;3k^5l^3 + 2k^2l^2 - 7kl$