Case 3. Q(x) Contains Irreducible Quadratic Factors, None Of Which Are Repeated Something like x2 +1 occurs in the factorization of Q(x). In this case we will have to write (Ax+B)/(x²+1) in the partial fraction decomposition. For example, A Bx +C Dx+ E (x- 2)(x2 +1)(x² +4) X -2 x2 +1 x2 +4 6. What are the forms (constant, linear, or quadratic) of the numerators in each fraction above? 7. How does the form of the numerator compare with its denominator? 8. Explain the differences in the form of the numerators for terms with irreducible quadratics (case 3) and repeating linear terms (case 2). 9. Evaluate the integral. 2x2 - x+4 x3+4x xp Case 4. Q(x) Contains Repeated Irreducible Quadratic Factors
Case 3. Q(x) Contains Irreducible Quadratic Factors, None Of Which Are Repeated Something like x2 +1 occurs in the factorization of Q(x). In this case we will have to write (Ax+B)/(x²+1) in the partial fraction decomposition. For example, A Bx +C Dx+ E (x- 2)(x2 +1)(x² +4) X -2 x2 +1 x2 +4 6. What are the forms (constant, linear, or quadratic) of the numerators in each fraction above? 7. How does the form of the numerator compare with its denominator? 8. Explain the differences in the form of the numerators for terms with irreducible quadratics (case 3) and repeating linear terms (case 2). 9. Evaluate the integral. 2x2 - x+4 x3+4x xp Case 4. Q(x) Contains Repeated Irreducible Quadratic Factors
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter10: Systems Of Equations And Inequalities
Section10.CR: Chapter Review
Problem 7CC
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Transcribed Image Text:Case 3. Q(x) Contains Irreducible Quadratic Factors, None Of Which Are Repeated
Something like x2 +1 occurs in the factorization of Q(x). In this case we will have to write (Ax+B)/(x²+1)
in the partial fraction decomposition. For example,
A
Bx +C
Dx+ E
(x- 2)(x2 +1)(x² +4)
X -2
x2 +1
x2 +4
6. What are the forms (constant, linear, or quadratic) of the numerators in each fraction above?
7. How does the form of the numerator compare with its denominator?
8. Explain the differences in the form of the numerators for terms with irreducible quadratics (case 3) and
repeating linear terms (case 2).
9. Evaluate the integral.
2x2 - x+4
x3+4x
xp
Case 4. Q(x) Contains Repeated Irreducible Quadratic Factors
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