If f(x) is a polynomial of degree less than 3, then prove that f(a) (x-a) |1 f(b) (x-b) f(c) (x-c) 1 a 1 b 1 c a a² b 6² 222 C f(x) (x-a)(x-b)(x-c)

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Exponential And Logarithmic Functions
Section: Chapter Questions
Problem 10CT
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Question
If f(x) is a polynomial of degree less than 3, then prove that
f(a)
(x-a) 1
f(b)
(x-b)
f(c)
(x-c)|
1
a
1 b
C
a
+1 b
L
C
a²
222
6²
=
f(x)
(x-a)(x-b)(x-c)
Transcribed Image Text:If f(x) is a polynomial of degree less than 3, then prove that f(a) (x-a) 1 f(b) (x-b) f(c) (x-c)| 1 a 1 b C a +1 b L C a² 222 6² = f(x) (x-a)(x-b)(x-c)
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