Thread: division polynomial problem?

1. division polynomial problem?

How would I do a problem like this?

$15m^3+26m^2-11m-6$
___________________
$5m-3$

I'd know how to do it if it was just divided by 5m, but what do I do with the negative 3? For example, let's say I split it up, and the first section is

$15m^3$
___________________
$5m-3$

that part would be $3m^2$ something, but then what would I do with that negative 3?

2. Originally Posted by deathtolife04
How would I do a problem like this?

$15m^3+26m^2-11m-6$
___________________
$5m-3$

...
Hello,

do long division:
Code:
( 15m^3 + 26m^2 - 11m - 6) ÷ (5m - 3) = 3m^2 + 7m + 2
-(15m^3 -  9m^2)
-----------------
35m^2 - 11m
-(35m^2 - 21m)
-------------
10m - 6
-(10m - 6)
---------
0
That means $(5m-3)$ is a factor of $15m^3+26m^2-11m-6$

Actually you can factor $3m^2+7m+2$ too.

3. Originally Posted by earboth
Hello,

do long division:
Code:
( 15m^3 + 26m^2 - 11m - 6) ÷ (5m - 3) = 3m^2 + 7m + 2
-(15m^3 -  9m^2)
-----------------
35m^2 - 11m
-(35m^2 - 21m)
-------------
10m - 6
-(10m - 6)
---------
0
That means $(5m-3)$ is a factor of $15m^3+26m^2-11m-6$

Actually you can factor $3m^2+7m+2$ too.
is that the only way to do it?
i don't remember ever learning that.

4. Originally Posted by deathtolife04
is that the only way to do it?
i don't remember ever learning that.
well, there is synthetic division, but i never really learned that . i'm fast enough with long division so i never felt the need to learn it

5. Originally Posted by earboth
Hello,

do long division:
Code:
( 15m^3 + 26m^2 - 11m - 6) ÷ (5m - 3) = 3m^2 + 7m + 2
-(15m^3 -  9m^2)
-----------------
35m^2 - 11m
-(35m^2 - 21m)
-------------
10m - 6
-(10m - 6)
---------
0
That means $(5m-3)$ is a factor of $15m^3+26m^2-11m-6$

Actually you can factor $3m^2+7m+2$ too.
ok I'm still really confused.
could someone maybe explain it a little more step by step?

also, wouldn't it be 17 and not 35?? cuz you subtract??

6. Originally Posted by deathtolife04
also, wouldn't it be 17 and not 35?? cuz you subtract??
you actually added. notice there is a minus sign in front of the brackets

7. Originally Posted by Jhevon
you actually added. notice there is a minus sign in front of the brackets

oooh ok gotcha