How to divide a polynomial by a monomial

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Division of polynomial by monomial = divide each term of a polynomial by the monomial and simplify.

For dividing a polynomial in one variable by a monomial in the same variable, we perform the following steps :

• Obtain the polynomial(Dividend) and the monomial(divisor).
• Arrange the terms of the dividend in the descending order of their exponents.
• Separate the each term using heart method.
• Divide each term of the polynomial be the given monomial by using the rules of division of a monomial by a monomial.

Some solved examples:

= (9m5/3m2) + (12m4/3m2) - (6m2/3m2)
= 3m3 + 4m2 - 2
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3) 24x3y + 20x2y2 - 4xy ÷ 2xy

Solution :
   24x3y + 20x2y2 - 4xy
= --------------------
        2xy

= (24x3y/2xy) + (20x2y2/2xy) - (4xy/2xy)
= 12x2 + 10xy - 2
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4) x + 2x2 + 3x4 - x5 ÷ by 2x

Solution :
First arrange all the terms in decreasing order of exponents
-x5 + 3x4 + 2x2 + x ÷ 2x

   -x5 + 3x4 + 2x2 + x
= --------------------
        2x
= (-x5/2x) + (3x4/2x) + (2x2/2x) + (x/2x)

= (-1/2) x4 + (3/2)x3 + x + 1/2
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5) 5x2 - 25x ÷ 5x

Solution :
First arrange all the terms in decreasing order of exponents
5x2 - 25x ÷ 5x

    5x( x - 5)
= ------------
          5x
= x -5

Division of Algebraic Expressions

• Division of Polynomial by Monomial
• Division of Polynomial by Binomial

Dividing a Polynomial by a Monomial: When dividing a polynomial by a monomial, divide EACH term of the polynomial by the monomial. Remember to use the quotient rule for exponents. When dividing a polynomial by a monomial, the number of terms in the polynomial equals the number of terms in the answer. When dividing by a monomial, numbers (or expressions) do not "cancel" and disappear! 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. Dividing a Polynomial by a Binomial: (also check out Factoring) When dividing a polynomial by a binomial, FACTOR completely both the numerator and denominator (the dividend and divisor) before reducing. Reduce the greatest common factors from the numerator and denominator. The terms in a binomial cannot be separated from one another when reducing. For example, in the binomial 4x - 1, the 4x cannot be reduced by itself. You must reduce the entire expression 4x - 1. Factor the numerator. Reduce the common factor of x + 3. Factor the numerator. Reduce the common factor of a - 5. Factor the numerator. Reduce the common factor y + 2. Factor the numerator. Factor the denominator. Reduce the common factor of x + 2. Sneaky one!! 7 - xand x - 7 are "almost" the same, except that the signs of the terms are opposite one another. To create a situation that will allow for reducing, factor out -1 from one of these binomials. NOTE: The re-posting of materials (in part or whole) from this site to the Internet is copyright violation and is not considered "fair use" for educators. Please read the "Terms of Use".

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