Dividing Polynomials
We will be examining polynomials divided by monomials and by binomials.
Steps for Dividing a Polynomial by a Monomial:
- 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. - Remember that numbers do not cancel and disappear! A number divided by itself is 1. It reduces to the number 1.
- 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:
- 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.
- Factor completely both the numerator and denominator before reducing.
- 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