Polynomial Long Division | MathHelp.com - Free Educational videos for Students in K-12 | Lumos Learning

Polynomial Long Division | MathHelp.com - Free Educational videos for Students in k-12


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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