Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Polynomial Division
To divide the polynomial \(4x^6 + 12x^4 - 12x^3\) by \(4x^3\), follow these steps:
**Problem:**
\[ \text{Divide:} \ \frac{4x^6 + 12x^4 - 12x^3}{4x^3} \]
**Solution:**
1. **Divide each term in the numerator by the term in the denominator:**
\[
\frac{4x^6}{4x^3} + \frac{12x^4}{4x^3} - \frac{12x^3}{4x^3}
\]
2. **Simplify each division separately:**
\[
= \left(4x^6 \div 4x^3\right) + \left(12x^4 \div 4x^3\right) - \left(12x^3 \div 4x^3\right)
\]
\[
= x^{6-3} + 3x^{4-3} - 3
\]
\[
= x^3 + 3x - 3
\]
**Result:**
\[ x^3 + 3x - 3 \]
This process of polynomial division helps to simplify complex polynomial expressions by breaking down each term separately.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6419df05-0cdf-40cf-9a07-cb413b8a1cc6%2F0dd2eb0c-edd8-42b3-8a9f-3c4703b01660%2F90jdxct_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Polynomial Division
To divide the polynomial \(4x^6 + 12x^4 - 12x^3\) by \(4x^3\), follow these steps:
**Problem:**
\[ \text{Divide:} \ \frac{4x^6 + 12x^4 - 12x^3}{4x^3} \]
**Solution:**
1. **Divide each term in the numerator by the term in the denominator:**
\[
\frac{4x^6}{4x^3} + \frac{12x^4}{4x^3} - \frac{12x^3}{4x^3}
\]
2. **Simplify each division separately:**
\[
= \left(4x^6 \div 4x^3\right) + \left(12x^4 \div 4x^3\right) - \left(12x^3 \div 4x^3\right)
\]
\[
= x^{6-3} + 3x^{4-3} - 3
\]
\[
= x^3 + 3x - 3
\]
**Result:**
\[ x^3 + 3x - 3 \]
This process of polynomial division helps to simplify complex polynomial expressions by breaking down each term separately.
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