(a) The space of cubic polynomials p(x) such that p(7) = 0 (b) The space of cubic polynomials p(x) such that p(7) = 0 and p(5) = 0 (c) The space of cubic polynomials p(x) such that p(7) = 0, p(5) = 0, and p(3) = 0 (d) The space of cubic polynomials p(x) such that p(7) = 0, p(5) = 0, p(3) = 0, and p(1) = 0

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 47E
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Please do part B,C,D and please show step by step and explain

2.21 Find the dimension of each.
(a) The space of cubic polynomials p(x) such that p(7) = 0
(b) The space of cubic polynomials p(x) such that p(7) = 0 and p(5) = 0
(c) The space of cubic polynomials p(x) such that p(7) = 0, p(5) = 0, and p(3) = 0
(d) The space of cubic polynomials p(x) such that p(7) = 0, p(5) = 0, p(3) = 0,
and p(1) = 0
Transcribed Image Text:2.21 Find the dimension of each. (a) The space of cubic polynomials p(x) such that p(7) = 0 (b) The space of cubic polynomials p(x) such that p(7) = 0 and p(5) = 0 (c) The space of cubic polynomials p(x) such that p(7) = 0, p(5) = 0, and p(3) = 0 (d) The space of cubic polynomials p(x) such that p(7) = 0, p(5) = 0, p(3) = 0, and p(1) = 0
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