Dividing a Polynomial by a Monomial
Dividing a polynomial by a single term (a monomial) means dividing each term of the polynomial by that monomial separately. The fraction bar distributes.
Within each term you divide the coefficients and subtract the exponents. It is the simplest kind of polynomial division and a warm-up for long division.
Split the fraction
A single denominator divides into every term of the numerator: .
So break the big fraction into one small fraction per term, then simplify each.
Divide each term
For each piece, divide the coefficients and subtract exponents: .
Line the simplified terms up in standard form. Every term of the numerator must be divided — do not skip the last one.
Worked examples
Example 1: term-by-term
Divide .
Answer:
Example 2: one term
Simplify .
Answer:
Try one yourself
Common questions
How do I divide the variable parts?
Subtract the exponents: . Divide the coefficients normally.
Do I divide every term?
Yes — the single denominator distributes to each term of the numerator. Missing the last term is a common slip.
How is this different from long division?
Dividing by a monomial is one clean step per term. Long division is needed when the divisor has more than one term.
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