##### Asked by: Kenan Guarido

asked in category: General Last Updated: 16th March, 2020# How do you divide polynomials by Monomials?

**divide**a

**polynomial**by a

**monomial**using the long

**division**algorithm, we

**divide**each term of the

**polynomial**(dividend) with the

**monomial**(divisor) to get the quotient. We will then multiply the divisor by the quotient and subtract the result from the dividend.

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Correspondingly, how do you divide by a Monomial?

To **divide** a **monomial** by a **monomial**, **divide** the coefficients (or simplify them as you would a fraction) and **divide** the variables with like bases by subtracting their exponents. To **divide** a polynomial by a **monomial**, **divide** each term of the polynomial by the **monomial**. Be sure to watch the signs!

Also Know, are fractions Monomials? However, **monomials** can be added or subtracted if they have like terms. The second expression appears not to be a **monomial** because a variable in the denominator of a **fraction** is the same as having that variable raised to a negative exponent. Remember, a **monomial** cannot have variables with negative exponents.

Similarly, you may ask, when dividing a polynomial by a Monomial each term of the polynomial is divided by the Monomial?

A number (or expression) **divided** by itself equals one. Another way of looking at "**dividing** by a **monomial**" is multiplying by the reciprocal of the **monomial**. See Example 2. **When dividing a polynomial** by a binomial, FACTOR completely both the numerator and denominator (the dividend and divisor) before reducing.

How do you divide exponents?

To **divide exponents** (or powers) with the same base, subtract the **exponents**. Division is the opposite of multiplication, so it makes sense that because you add **exponents** when multiplying numbers with the same base, you subtract the **exponents** when **dividing** numbers with the same base.