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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Question
![### Factoring Polynomials
1. **Problem:** Factor \( 64x^3 - 125 \).
This problem involves factoring a difference of cubes. The expression \( 64x^3 - 125 \) can be rewritten using the formula for factoring a difference of cubes, which is:
\[
a^3 - b^3 = (a - b)(a^2 + ab + b^2)
\]
In this case, \( a = 4x \) and \( b = 5 \) since \( (4x)^3 = 64x^3 \) and \( 5^3 = 125 \).
Thus, the factored form of the polynomial is:
\[
64x^3 - 125 = (4x - 5)(16x^2 + 20x + 25)
\]
Remember, this technique is useful for factoring any difference of cubes and involves identifying both components of the cubes and substituting them back into the formula.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7760b96-c8d9-4d9b-b2e3-c9194135283a%2F91184031-4406-498e-bcd8-8d8edbab1f35%2F2tde5gs.jpeg&w=3840&q=75)
Transcribed Image Text:### Factoring Polynomials
1. **Problem:** Factor \( 64x^3 - 125 \).
This problem involves factoring a difference of cubes. The expression \( 64x^3 - 125 \) can be rewritten using the formula for factoring a difference of cubes, which is:
\[
a^3 - b^3 = (a - b)(a^2 + ab + b^2)
\]
In this case, \( a = 4x \) and \( b = 5 \) since \( (4x)^3 = 64x^3 \) and \( 5^3 = 125 \).
Thus, the factored form of the polynomial is:
\[
64x^3 - 125 = (4x - 5)(16x^2 + 20x + 25)
\]
Remember, this technique is useful for factoring any difference of cubes and involves identifying both components of the cubes and substituting them back into the formula.
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