If f(x) is a polynomial of degree less than 3, then prove that f(a) (x-a) 1 a +1 b f(b) (x-b) f(c) (x-c)| a 1 b C с a²| 6² c² = f(x) (x-a)(x-b)(x-c)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 3E
icon
Related questions
Question
If f(x) is a polynomial of degree less than 3, then prove that
f(a)
(x-a) 1 a
+1 b
f(b)
(x-b)
f(c)
(x-c)|
a
1 b
1
C
с
a²
6²
c²
=
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 a +1 b f(b) (x-b) f(c) (x-c)| a 1 b 1 C с a² 6² c² = f(x) (x-a)(x-b)(x-c)
Expert Solution
steps

Step by step

Solved in 4 steps with 4 images

Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax