What to Do 
How to Do It 
1. Divide a
binomial by a monomial using the definition of division,
the distributive property
and the laws of the exponents. 

2. Divide 6a^{5}  15a^{7} by  3a using
the definition of division,
the distributive property
and the laws of the exponents.. 

3. Divide a
polynomial by a monomial in the same
way, watching signs and powers.
Divide each term using the distributive property.
Reduce each fraction to lowest terms: 

4.
Simplify the numerator and divide polynomial
by a monomial in the same way, watching signs
and powers.
Divide the polynomial by the monomial
Divide each term using the distributive property.
Reduce each fraction to lowest terms: 

Divide a polynomial by a binomial using the
methods of long division.


The polynomial must be arranged in
descending order with spaces left as
placeholders for any missing powers. 

Divide the first term of the binomial exactly into
the first term of the polynomial. Multiply the
resulting quotient term times all of the binomial.


Subtract this product by the rules of algebra,
change signs and add →
Write the resulting sum and continue : 

Bring down the next polynomial term
and repeat these steps.


Look at the first term of the next binomial:
Divide x into  3x →
Multiply divisor binomial and subtract this product
change signs and add 

When the
remainder of the division of a polynomial by a binomial is equal to
zero,
the divisor and quotient are called exact divisors or factors of the polynomial. Check by multiplying the divisor by the quotient : (x − 2)( x − 3) = x^{2} − 5x + 6 