Dividing Polynomials

Dividing Polynomials

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
   * 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.

Think about it:

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.

Example 1:
Notice that the x+1 was reduced as a “set”.

Example 2:

Example 3:

Example 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)

Read More:

• What is a Polynomial?
• Types of Polynomials
• Monomials, Binomials, and Polynomials
• Adding Polynomials
• Subtracting Polynomials
• Polynomials – Long Division
• Degree (of an Expression)
• Special Binomial Products
• Multiplying Binomials
• Difference of Two Cubes
• Polynomial Remainder Theorem
• Factoring in Algebra
• Factorization of Polynomials Using Factor Theorem
• How do you use the factor theorem?
• How to factorise a polynomial by splitting the middle term?
• Review Factoring Polynomials
• Zeros of a Polynomial Function
• Factors and Coefficients of a Polynomial
• Roots of Polynomials: Sums and Products
• Review Factoring Polynomials
• Solving Polynomial Equations of Higher Degree
• Examining Graphs of Polynomial Equations of Higher Degree