Use Division to Write the Rational Function in the Form $$\frac { 4 x ^ { 3 } + 8 x ^ { 2 } + 5 x - 7 } { 2 x ^ { 2 } - x - 1 }$$

question 289

Multiple Choice

Use division to write the rational function in the form q(x) + r(x) /d(x) , where the degree of r(x) is less than the degree of
d(x) . Then find the partial fraction decomposition of r(x) /d(x) .
- $$\frac { 4 x ^ { 3 } + 8 x ^ { 2 } + 5 x - 7 } { 2 x ^ { 2 } - x - 1 }$$

• A) \(2 x + 5 + \frac { 16 / 3 } { 2 x + 1 } + \frac { 10 / 3 } { x - 1 }\)
• B) \(2 x - 5 - \frac { 5 / 3 } { 2 x + 1 } + \frac { 1 / 3 } { x - 1 }\)
• C) \(2 x + 5 - \frac { 7 / 3 } { 2 x + 1 } + \frac { 13 / 3 } { x - 1 }\)
• D) \(2 x - 5 + \frac { 13 } { 2 x + 1 } + \frac { 7 } { x - 1 }\)

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Definitions:

Two-Tailed Test

A statistical test where the significance area is on both ends of the distribution, examining if a sample falls outside a specific value range on either side.

Null Hypothesis

A hypothesis used in statistics that proposes no significant difference or effect, serving as the default assumption to be tested against an alternative hypothesis.

Test Statistic

A value determined from sample data, used to make decisions on a hypothesis in statistical testing.

Level Of Significance

A threshold in hypothesis testing, representing the probability of rejecting a true null hypothesis, typically denoted by alpha.