12. Find values of the constants A, B, C, and D that make the following equation an identity (i.e., true for all values of x). C 3x³+4x² - 6x (x² + 2x + 2)(x² - 1) = Ax + B x² + 2x + 2 + X- + D x+1
12. Find values of the constants A, B, C, and D that make the following equation an identity (i.e., true for all values of x). C 3x³+4x² - 6x (x² + 2x + 2)(x² - 1) = Ax + B x² + 2x + 2 + X- + D x+1
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.CT: Chapter Test
Problem 20CT
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Question
ind values of the constanta A,B,C, and D that make the following equation an identity (i.e.,true for all values of x) by Gauss-Jordan
![T2. Find values of the constants A, B, C, and D that make the
following equation an identity (i.e., true for all values of x).
C
3x³+4x²
6x
(x² + 2x + 2)(x² - 1)
-
=
Ax + B
x² + 2x + 2
+
+
D
x+1
[Hint: Obtain a common denominator on the right, and then equate
corresponding coefficients of the various powers of x in the two
numerators. Students of calculus will recognize this as a problem
in partial fractions.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Facee6d3c-64a8-4041-9bdd-fa02f4d4c7a1%2Fafee0353-5b3c-489a-bdf7-653949a63e7c%2Fodrp7dy_processed.png&w=3840&q=75)
Transcribed Image Text:T2. Find values of the constants A, B, C, and D that make the
following equation an identity (i.e., true for all values of x).
C
3x³+4x²
6x
(x² + 2x + 2)(x² - 1)
-
=
Ax + B
x² + 2x + 2
+
+
D
x+1
[Hint: Obtain a common denominator on the right, and then equate
corresponding coefficients of the various powers of x in the two
numerators. Students of calculus will recognize this as a problem
in partial fractions.]
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