

We will be examining polynomials
divided by monomials and by binomials.

Steps for Dividing a Polynomial by a
Monomial:
1.
Divide each term of the polynomial by the monomial. 
a) Divide numbers
(coefficients)
b) Subtract exponents 
Keep
this in mind


* The number of terms in the polynomial equals the number
of terms in the answer when dividing by a monomial. 
2. Remember that numbers do not cancel and
disappear! A number divided by itself
is 1. It reduces to the number
1. 
3.
Remember to write the appropriate sign in between
the terms. 

Example: 


The polynomial on
the top has 3 terms and the answer has 3 terms. 

Notice how the numbers (the coefficients)
were divided. 
Answer:

Notice how the exponents were subtracted.
Notice how the last term reduced to one. 

Think about it: 

Dividing by a
number is the same process as multiplying by the reciprocal of
that number. 


Notice how we used
the reciprocal of 4x^{2} 
Answer:

Now the reciprocal
was distributed across the parentheses and the problem proceeds
as in the example above. 

Steps for Dividing a Polynomial by a
Binomial:
1.
Remember that the
terms in a binomial cannot be separated from one another
when reducing.
For example, in the binomial 2x + 3, the 2x
can never be reduced unless the entire
expression 2x + 3 is
reduced. 
2. Factor completely both
the numerator and denominator before reducing. 
3.
Divide both the numerator and denominator by their
greatest common factor. 
Examples:
(see more under "Factoring"
section)
1. 

Notice that the x+1
was reduced as a "set". 
2. 


3. 


4. 

Tricky strategy: Notice that the 1
was factored out of the numerator to create a binomial
compatible with the one in the denominator.
2  x = 1(x  2) 


If you are solving multiple choice
questions, you can use the calculator to
"check" your work with polynomials.
You can use a Numerical Checking process:
Numerical Process
or
You can use an Equation Checking process::
Equation Process 

