2. In the following, write the rational function as a combination of factors like those appearing in (4) and/or (5) of Section 8.4, without finding the numerical values of the constants A1,..., B1, ..., C1, ... 6x2 – 4x +1 (a) (x – 2)3 x³ + 2x2 + 3x + 4 (b) x4 - 16

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Chapter4: Polynomial And Rational Functions
Section4.6: Rational Functions
Problem 90E
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2. In the following, write the rational function as a combination of factors like those appearing in (4)
and/or (5) of Section 8.4, without finding the numerical values of the constants A1,., B1, ., C1, ...
6x2
(a)
(x – 2)3
x3 + 2x2 + 3x + 4
(b)
— 4х + 1
x4
16
Transcribed Image Text:2. In the following, write the rational function as a combination of factors like those appearing in (4) and/or (5) of Section 8.4, without finding the numerical values of the constants A1,., B1, ., C1, ... 6x2 (a) (x – 2)3 x3 + 2x2 + 3x + 4 (b) — 4х + 1 x4 16
After performing operations (i) and (ii) we obtain a rational function g such
that the denominator of g(x) is a product of constants, factors of the form (ax + b)",
and factors of the form (ax² + bx +c)° (where ax² + bx + c cannot be factored). The
final step in the preparation involves equating g(x) with a sum of terms arising from
the factors appearing in the denominator of g(x). For every factor (ax + b)"
appearing in the denominator of g(x) we include an expression of the form
A1
A2
А,
+... +
(4)
ах + b
(ах + b)?
(ах + b)"
where A1, A2, ..., A, are constants to be determined. For every factor of the form
(ax + bx + c)° we include an expression of the form
B1x + C,
B2x + C2
B,x + C,
+
+
(5)
...
ax² + bx + c
(ах? + bx + с)?
(ах2 + bx + с)s
Transcribed Image Text:After performing operations (i) and (ii) we obtain a rational function g such that the denominator of g(x) is a product of constants, factors of the form (ax + b)", and factors of the form (ax² + bx +c)° (where ax² + bx + c cannot be factored). The final step in the preparation involves equating g(x) with a sum of terms arising from the factors appearing in the denominator of g(x). For every factor (ax + b)" appearing in the denominator of g(x) we include an expression of the form A1 A2 А, +... + (4) ах + b (ах + b)? (ах + b)" where A1, A2, ..., A, are constants to be determined. For every factor of the form (ax + bx + c)° we include an expression of the form B1x + C, B2x + C2 B,x + C, + + (5) ... ax² + bx + c (ах? + bx + с)? (ах2 + bx + с)s
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