Use Division to Write the Rational Function in the Form $$\frac { 4 x ^ { 3 } + 8 x ^ { 2 } - 6 x + 2 } { 2 x ^ { 2 } - x - 1 }$$

question 167

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) .
- $$\frac { 4 x ^ { 3 } + 8 x ^ { 2 } - 6 x + 2 } { 2 x ^ { 2 } - x - 1 }$$

• A) \(2 x + 5 - \frac { 13 / 3 } { 2 x + 1 } + \frac { 8 / 3 } { x - 1 }\)
• B) \(2 x - 5 - \frac { 13 } { 2 x + 1 } + \frac { 7 } { x - 1 }\)
• C) \(2 x + 5 - \frac { 7 / 3 } { 2 x + 1 } + \frac { 13 / 3 } { x - 1 }\)
• D) \(2 x - 5 - \frac { 5 / 3 } { 2 x + 1 } + \frac { 1 / 3 } { x - 1 }\)

---

Definitions:

Harsh Verbal Discipline

The use of aggressive or demeaning language by a parent or caretaker towards a child, which can negatively affect the child’s self-esteem and behavior.

Early Childhood

The period of a child's life from birth to the age of eight, focusing on holistic development including physical, cognitive, and social-emotional growth.

Developmentally Supportive

Practices or environments that promote and enhance an individual's developmental progress and well-being according to their age and abilities.

Conflict

A serious disagreement or argument, typically a prolonged one, which can occur between individuals, groups, or within an individual.