Podcast
Questions and Answers
What is the main purpose of polynomial long division?
What is the main purpose of polynomial long division?
- To add two polynomials together
- To find the roots of a polynomial
- To simplify a polynomial expression
- To divide one polynomial by another and find the quotient and remainder (correct)
In what order should the dividend and divisor be written in polynomial long division?
In what order should the dividend and divisor be written in polynomial long division?
- Random order
- Ascending order of degrees
- Alphabetical order of terms
- Descending order of degrees (correct)
What is the result of repeating steps 2 and 3 in polynomial long division?
What is the result of repeating steps 2 and 3 in polynomial long division?
- The dividend and divisor are switched
- A new polynomial is obtained (correct)
- The quotient and remainder are obtained
- The operation is stopped
What is a key concept in polynomial long division?
What is a key concept in polynomial long division?
How can the quotient and remainder be checked?
How can the quotient and remainder be checked?
What is one of the uses of polynomial long division?
What is one of the uses of polynomial long division?
Study Notes
Polynomial Long Division
Definition: Polynomial long division is a method for dividing one polynomial by another and finding the quotient and remainder.
Steps:
- Write the dividend (the polynomial being divided) and the divisor (the polynomial by which we are dividing) in the correct order.
- The dividend should be written in descending order of degrees, and the divisor should be written in descending order of degrees.
- ** Divide the leading term of the dividend by the leading term of the divisor.**
- This will give the first term of the quotient.
- Multiply the divisor by the term found in step 2 and subtract the product from the dividend.
- This will give a new polynomial.
- Repeat steps 2 and 3 until the degree of the remainder is less than the degree of the divisor.
- The final quotient and remainder are the result of the division.
Example:
Divide x^2 + 3x - 2 by x - 1.
| Quotient | Remainder | |
|---|---|---|
| 1 | x + 4 | -6 |
Key Concepts:
- The degree of the remainder must be less than the degree of the divisor.
- The quotient and remainder can be checked by multiplying the divisor by the quotient and adding the remainder to ensure the original dividend is obtained.
- Polynomial long division can be used to factor polynomials, find roots, and perform other operations.
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Description
Learn the steps and concepts involved in polynomial long division, including the degree of remainders, quotients, and dividends, with examples and key concepts explained.
