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Answer:
Dividing polynomials involves dividing one polynomial expression by another. The process is similar to long division or synthetic division that you might have learned for dividing numbers, but it involves terms with variables. Here's a general overview of the steps:
1. **Write the Division:**
- Write the dividend (the polynomial you're dividing) inside the long division symbol.
- Write the divisor (the polynomial you're dividing by) outside the division symbol.
2. **Divide the Leading Terms:**
- Divide the leading term of the dividend by the leading term of the divisor.
- Write the result above the long division symbol.
3. **Multiply and Subtract:**
- Multiply the entire divisor by the result obtained in step 2.
- Subtract this product from the dividend.
4. **Bring Down the Next Term:**
- Bring down the next term from the dividend.
5. **Repeat:**
- Repeat steps 2-4 until you've brought down all the terms of the dividend.
6. **Final Result:**
- The result of the division is the quotient written above the long division symbol, and any remainder, if present.
For example, let's say you want to divide \(2x^3 + 5x^2 - 3x + 7\) by \(x - 2\). The steps would involve dividing the leading term, multiplying, subtracting, and repeating until all terms are brought down.
Keep in mind that some polynomials may not divide evenly, resulting in a remainder. In that case, you would express the result as a quotient plus the remainder over the divisor.
Dividing polynomials is a fundamental operation in algebra and is often used in various mathematical applications.
Step-by-step explanation:
