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10.5 – Dividing Polynomials
Key Terms
 Dividend – The number to be divided (numerator).
 Divisor – The number being divided by (denominator).
 Quotient – The result of a division problem (answer).
 Remainder – A number left over after dividing whole numbers.
 The letter r is sometimes used to represent a remainder.
Review
Remember… 
 Constant terms have a degree of zero
 Ex.
 Ex.
 For long division, use DMS, and perform these steps over and over until you are done!
 Divide
 Multiply
 Subtract

Notes
What is Division? 
 When you divide, you separate a total amount into equal groups to find the number of groups or to find the number in each group.
 You cannot divide by zero because there is no way to separate a total into zero groups or into groups with zero items.
 Ex. If I have 33 oreos and 14 students, I could divide the oreos by the number of students to see how many cookies each student would receive. There would be a remainder of 5, as each student would receive 2 cookies each.
 Ex. If I have 58 students who want to play Capture the Flag, and we only want 2 teams, how many students could be on each team? You’d want to divide the students into 2 groups! There would be 29 students on each team!

Parts of a Division Problem 

When to Stop Dividing 
 Ask yourself:
 Is the degree (exponent) of the remainder less than the degree (exponent) of the divisor?
 If no, I should keep dividing.
 If yes, I should stop dividing.
 Example: For , the quotient is (3x2) remainder 1.
 Remainder 1 has a degree of zero.
 Zero is less than , so stop dividing!

Check Your Work 
 Division and multiplication are inverse operations.
 Use multiplication to check division.
 divisor • quotient = dividend
 Example (using the same problem in the example above)
 If the answer has a remainder, you need addition to check the answer.
 (divisor • quotient) + remainder = dividend

Examples
Important!
Practice (Apex Study 10.5)
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