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1. Factor the polynomial completely using the given factor 4 2 2 and division: x - 3x 3 - 36x +68x + 240; x - 4x 12

1. Factor the polynomial completely using the given factor 4 2 2 and division: x - 3x 3 - 36x +68x + 240; x - 4x 12

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Factor the polynomial completely using the given factor and division: \(x^4 - 3x^3 - 36x^2 + 68x + 240; \quad x^2 - 4x - 12\) **Explanation:** This problem involves factoring a polynomial completely using a provided factor of \(x^2 - 4x - 12\). The task includes polynomial division to break down the given polynomial into simpler components. ### Steps: 1. **Identify the Given Factor:** - The polynomial \(x^2 - 4x - 12\) is provided as a factor. 2. **Polynomial Long Division or Synthetic Division:** - Use either polynomial long division or synthetic division to divide \(x^4 - 3x^3 - 36x^2 + 68x + 240\) by \(x^2 - 4x - 12\). 3. **Find the Quotient:** - The quotient obtained after division, when multiplied with the given factor, should give the original polynomial. 4. **Factor Completely:** - Check if the quotient and any resultant polynomials can be factored further into simpler binomials or trinomials.
Transcribed Image Text:1. Factor the polynomial completely using the given factor and division: \(x^4 - 3x^3 - 36x^2 + 68x + 240; \quad x^2 - 4x - 12\) **Explanation:** This problem involves factoring a polynomial completely using a provided factor of \(x^2 - 4x - 12\). The task includes polynomial division to break down the given polynomial into simpler components. ### Steps: 1. **Identify the Given Factor:** - The polynomial \(x^2 - 4x - 12\) is provided as a factor. 2. **Polynomial Long Division or Synthetic Division:** - Use either polynomial long division or synthetic division to divide \(x^4 - 3x^3 - 36x^2 + 68x + 240\) by \(x^2 - 4x - 12\). 3. **Find the Quotient:** - The quotient obtained after division, when multiplied with the given factor, should give the original polynomial. 4. **Factor Completely:** - Check if the quotient and any resultant polynomials can be factored further into simpler binomials or trinomials.
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