Dividing a Polynomial by a Monomial

Description/Explanation/Highlights

Video Description

This video explains how to divide a polynomial by a monomial.

Steps and Key Points to Remember

To divide a polynomial by a monomial, follow these steps:

  1. To divide a polynomial by a monomial, first rewrite the problem as a fraction. For example, rewrite \((9x^4y^3+6x^3y^2-15x^2y)\div(3xy)\) to \(\frac{\displaystyle 9x^4y^3+6x^3y^2-15x^2y}{\displaystyle 3xy}\)
  2. Next, write each term in the numerator separately over the denominator. \(\frac{\displaystyle 9x^4y^3}{\displaystyle 3xy}+\frac{\displaystyle 6x^3y^2}{\displaystyle 3xy}-\frac{\displaystyle 15x^2y}{\displaystyle 3xy}\)
  3. Apply the rules of exponents to each part. Divide 9 by 3 then apply the rule of exponents that apply to division and subtract the exponents of x and y. The resulting first term will be \(3x^3y^2\). Doing the same with each piece will get the following result \(3x^3y^2+2x^2y-5x\).
  4. There are no like terms but if they exist, like terms should be combined.
  5. When dividing, some variables may “cancel” and not appear in the final result. Here is an example: \(\frac{\displaystyle 20x^4y^2z-16xyz+4xyz}{\displaystyle 4xyz}=\frac{\displaystyle 20x^4y^2z}{\displaystyle 4xyz}-\frac{\displaystyle 16xyz}{\displaystyle 4xyz}+\frac{\displaystyle 4xyz}{\displaystyle 4xyz}=5x^3y-4+1=5x^3y-3\). In this example, the \(z\) canceled in the first term, all three variables canceled in the second and third terms, and the third term became = 1. The constants were then combined to equal -3 in the final answer.

Here are some key points to keep in mind when dividing a polynomial by a monomial.

  • Use this method when dividing a polynomial with any number of terms by a monomial.
  • Write the division problem as a fraction with the polynomial in the numerator and the monomial in the denominator.
  • Rewrite the problem with each term in the numerator written over its own denominator.
  • Apply the rules of exponents to simplify each term.
  • Combine like terms, if they exist, to finish the problem.

Video Highlights

  • 00:00 Introduction
  • 00:06 \((9x^4y^3+6x^3y^2-15x^2y)\div(3xy)\) example of how to rewrite and solve a polynomial divided by a monomial.
  • 02:25 \(\frac{\displaystyle 20x^4y^2z-16xyz+4xyz}{\displaystyle 4xyz}\) example of a division problem where variables cancel.
  • 04:15 Conclusion
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