Polynomial Long Division | MathHelp.com - By MathHelp.com
Transcript
00:0-1 | in this example it's tempting to divide X squared plus | |
00:04 | five x minus six by X plus one by first | |
00:08 | factoring X squared plus five X minus six . The | |
00:13 | factors of negative six that add to positive five are | |
00:17 | positive six and negative one . So we have X | |
00:21 | plus six times x minus one over X plus one | |
00:27 | . Notice however , that nothing cancels in this situation | |
00:32 | , we need a different method of dividing the polynomial | |
00:35 | . So we use long division . In other words | |
00:39 | we rewrite X squared plus five X minus six , | |
00:44 | divided by X plus one as X plus one divided | |
00:48 | into X squared plus five x minus six . Now | |
00:54 | our first step in the long division is to determine | |
00:57 | how many times X goes into X squared . Since | |
01:01 | X goes into X squared X times we write an | |
01:05 | X above the X squared , just like we do | |
01:09 | with regular long division . Next we multiply the X | |
01:13 | times the X plus one in the divisor to get | |
01:17 | X squared plus X . And we write the X | |
01:20 | squared plus X underneath the X squared plus five X | |
01:26 | . Next we subtract X squared plus X from X | |
01:30 | squared plus five X . And watch out for this | |
01:33 | step . It's an area where most of the common | |
01:36 | mistakes in these types of problems are made . Instead | |
01:41 | of subtracting I would change the sign of each term | |
01:45 | in X squared plus X . So we have negative | |
01:49 | X squared plus negative X . Then add the columns | |
01:54 | . So we have X squared plus negative X squared | |
01:58 | which cancels out and positive five X plus negative X | |
02:03 | . Which is positive for X . Next we bring | |
02:07 | down the -6 just like in regular long division . | |
02:12 | Now we need to determine how many times X goes | |
02:16 | into forex . Since X goes into four x 4 | |
02:20 | times We write a positive four in our answer . | |
02:25 | Next we multiply positive four times X plus one to | |
02:29 | get four X plus four . And we write the | |
02:33 | four X plus four underneath the four x minus six | |
02:37 | . Next we subtract four X plus four from four | |
02:41 | x minus six . In other words we change the | |
02:45 | signs on four X plus four to negative four X | |
02:49 | plus negative four and we add four X plus negative | |
02:53 | four X cancels out and negative six plus negative four | |
02:58 | is negative 10 . And since there are no other | |
03:01 | numbers to bring down , we have a remainder of | |
03:04 | -10 . Finally remember from the previous example that we | |
03:10 | add the remainder over the divisor to the quotient . | |
03:15 | In other words we add negative 10 over X +12 | |
03:20 | X plus four and we have X plus four plus | |
03:24 | negative 10 over X plus one . So X squared | |
03:28 | plus five X minus six , divided by X plus | |
03:32 | one simplifies to X plus four plus negative 10 over | |
03:38 | X plus one . |
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