Can you divide the polynomial by the monomial? How does this relate to factoring?
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James Sousa: Dividing Polynomials by Monomials
Guidance
Recall that a monomial is an algebraic expression that has only one term. So, for example, , 8, –2, or are all monomials because they have only one term. The term can be a number, a variable, or a combination of a number and a variable. A polynomial is an algebraic expression that has more than one term.
When dividing polynomials by monomials, it is often easiest to separately divide each term in the polynomial by the monomial. When simplifying each mini-division problem, don't forget to use exponent rules for the variables. For example,
.
Remember that a fraction is just a division problem!
Example A
What is ?
Solution: This is the same as . Divide each term of the polynomial numerator by the monomial denominator and simplify.
Therefore, .
Example B
What is ?
Solution: Divide each term of the polynomial numerator by the monomial denominator and simplify. Remember to use exponent rules when dividing the variables.
Therefore, .
Example C
What is ?
Solution: This is the same as . Divide each term of the polynomial numerator by the monomial denominator and simplify. Remember to use exponent rules when dividing the variables.
Therefore, .
Concept Problem Revisited
Can you divide the polynomial by the monomial? How does this relate to factoring?
This process is the same as factoring out a from the expression .
Therefore, .
Vocabulary
- Divisor
- A divisor is the expression in the denominator of a fraction.
- Monomial
- A monomial is an algebraic expression that has only one term. , 8, –2, or are all monomials because they have only one term.
- Polynomial
- A polynomial is an algebraic expression that has more than one term.
Guided Practice
Complete the following division problems.
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Answers:
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Practice
Complete the following division problems.