2 Consider the set S = {x² + 1, 2x − 2, −x² + x}. The set S spans P2. If t(x) = 5x² + x + 2 € P₂, then t can be written as a linear combination of elements of S. That is, t(x) = Determine a, b, and c a = = a · (x² + 1) + b · (2x − 2) + c · (–x² + x). b = C = Question Help: Video Message instructor Post to forum

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.3: The Remainder And Factor Theorems; Synthetic Division
Problem 120E
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2
Consider the set S = {x² + 1, 2x − 2, −x² + x}. The set S spans P2.
If t(x) = 5x² + x + 2 € P₂,
then t can be written as a
linear combination of elements of S.
That is,
t(x) =
Determine a, b, and c
a =
= a ·
(x² + 1) + b · (2x − 2) + c · (–x² + x).
b
=
C =
Question Help: Video Message instructor Post to forum
Transcribed Image Text:2 Consider the set S = {x² + 1, 2x − 2, −x² + x}. The set S spans P2. If t(x) = 5x² + x + 2 € P₂, then t can be written as a linear combination of elements of S. That is, t(x) = Determine a, b, and c a = = a · (x² + 1) + b · (2x − 2) + c · (–x² + x). b = C = Question Help: Video Message instructor Post to forum
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