For the polynomial below, 2 is a zero. h(x)=x'+4x+ 6x- 36 Express h (x) as a product of linear factors.
For the polynomial below, 2 is a zero. h(x)=x'+4x+ 6x- 36 Express h (x) as a product of linear factors.
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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Not the (x-2)
![For the polynomial below, 2 is a zero.
\[ h(x) = x^3 + 4x^2 + 6x - 36 \]
Express \( h(x) \) as a product of linear factors.
\[ h(x) = (x - 2)(x^2 + 6x + 18) \]
Explanation:
- The polynomial \( h(x) = x^3 + 4x^2 + 6x - 36 \) is given, with 2 as a known zero.
- To express \( h(x) \) in terms of linear factors, factor out \( (x - 2) \).
- The remaining quadratic \( x^2 + 6x + 18 \) can be further analyzed to find additional zeros or express it as a product of linear terms if possible.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29ce3a4c-cb07-4c4c-bb91-a57b2d1f76d3%2F1766cb31-dc46-43bd-83af-a2bfdf3fb6be%2Fmm7q097_processed.jpeg&w=3840&q=75)
Transcribed Image Text:For the polynomial below, 2 is a zero.
\[ h(x) = x^3 + 4x^2 + 6x - 36 \]
Express \( h(x) \) as a product of linear factors.
\[ h(x) = (x - 2)(x^2 + 6x + 18) \]
Explanation:
- The polynomial \( h(x) = x^3 + 4x^2 + 6x - 36 \) is given, with 2 as a known zero.
- To express \( h(x) \) in terms of linear factors, factor out \( (x - 2) \).
- The remaining quadratic \( x^2 + 6x + 18 \) can be further analyzed to find additional zeros or express it as a product of linear terms if possible.
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