1. Long Hand Division
We know how to add, subtract, and multiply
polynomials. The only thing left to learn how to do
is divide.
The problems will look like these:
(m2 – 7m – 11) ÷ (m – 8)
or
m2 – 7m – 11
m–8
2. Long Hand Division
m2 – 7m – 11
m–8
The first polynomial is always your dividend
Quotient
Divisor Dividend
Divisor is what you are dividing by, dividend is what
you are splitting up, and quotient is the answer.
3. Long Hand Division
m2 – 7m – 11
m–8
The first polynomial goes inside
m – 8 m2 – 7m – 11
4. Long Hand Division
m – 8 m2 – 7m – 11
We want make the first terms of each polynomial
match.
So what do we multiply m by to get m2…. m
5. Long Hand Division
m
m – 8 m2 – 7m – 11
m2 – 8m
Now multiply m by both terms in the divisor.
6. Long Hand Division
m
m – 8 m2 – 7m – 11
- (m2 – 8m)
1m
Since we are dividing, we now subtract our product
from the dividend. m2 and m2 will cancel (which is
what we want). -7m – -8m = -7m + 8m = 1m
To continue dividing bring down last term in
dividend.
7. Long Hand Division
m
m – 8 m2 – 7m – 11
- (m2 – 8m)
1m – 11
Again, we want the first two terms to match. So
what do we multiply m by to make m….. +1
8. Long Hand Division
m + 1
m – 8 m2 – 7m – 11
- (m2 – 8m)
1m – 11
m–8
Distribute the 1 to both terms in the divisor.
9. Long Hand Division
m + 1
m – 8 m2 – 7m – 11
- (m2 – 8m)
1m – 11
-(m–8)
-3
Since we are dividing, we now subtract. m and m
will cancel (which is what we want).
-11 – -8 = -11 + 8 = -3 (this is our remainder)
13. Long Hand Division
Now click on the link below to view a you tube
presentation of how to divide polynomials by hand.
http://www.youtube.com/watch?v=smsKMWf8ZCs
