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10.5 – Dividing Polynomials
- 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.
|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!
|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 (3x-2) 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
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