Consider a polynomial p₁(x) = ao+a₁2+...+ ª₂z² = [ªo a₁ ... an] (x) and a constant z. Synthetic division gives us [bn (2) = an bx (2) = a + 2bx+1(3) for k=n-1,n-2,...,0. Prove that p₁(x) = (x − 2)qn−1(x; 2) + bo(2) where qn-1 (z; 2) = [b₁(2) b₂(2). b₁(z)](x).
Consider a polynomial p₁(x) = ao+a₁2+...+ ª₂z² = [ªo a₁ ... an] (x) and a constant z. Synthetic division gives us [bn (2) = an bx (2) = a + 2bx+1(3) for k=n-1,n-2,...,0. Prove that p₁(x) = (x − 2)qn−1(x; 2) + bo(2) where qn-1 (z; 2) = [b₁(2) b₂(2). b₁(z)](x).
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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![Consider a polynomial p₁(x) = ao+a₁2x +...+ ª₂x² = [ªo a₁ an] (x) and a constant
z. Synthetic division gives us
...
[b₁ (2)=a₂
[bk (2) = ak + zbk+1(2) for k=n-1,n-2,...,0.
Prove that pn(x) = (x − 2)qn-1(x; 2) + bo(z) where qn-1(x; 2) = [b₁(2) b₂(2)... bn(z)](x).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9f5f186b-a988-42dc-990a-dec6263b0762%2Fbd419264-e609-4447-b419-25766c61f325%2Fr2y6xr_processed.png&w=3840&q=75)
Transcribed Image Text:Consider a polynomial p₁(x) = ao+a₁2x +...+ ª₂x² = [ªo a₁ an] (x) and a constant
z. Synthetic division gives us
...
[b₁ (2)=a₂
[bk (2) = ak + zbk+1(2) for k=n-1,n-2,...,0.
Prove that pn(x) = (x − 2)qn-1(x; 2) + bo(z) where qn-1(x; 2) = [b₁(2) b₂(2)... bn(z)](x).
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