Use the Rational Root Theorem and the Factor Theorem to Help

question 46

Multiple Choice

Use the rational root theorem and the factor theorem to help solve the equation. Be sure that the number of solutions for the equation agrees with property of number solutions of a polynomial equation, taking into account multiplicity of solutions. $2 x ^ { 4 } + x ^ { 3 } - 16 x ^ { 2 } - 3 x + 30 = 0$

• A) \(\left\{ - \frac { 5 } { 2 } , 2 , \pm \sqrt { 3 } \right\}\)
• B) \(\left\{ - \frac { 3 } { 2 } , - 2 , \pm \sqrt { 3 } \right\}\)
• C) \(\left\{ - \frac { 5 } { 2 } , - 1 \pm \sqrt { 3 } \right\}\)
• D) \(\left\{ - \frac { 9 } { 2 } , 1 \pm \sqrt { 3 } \right\}\)
• E) \(\left\{ - \frac { 5 } { 2 } , - 2 , \pm \sqrt { 3 } \right\}\)

---

Definitions:

Special Materials

Unique or unusual materials required for specific production processes or products, often implying additional cost or procurement effort.

Step-fixed Costs

Expenses that remain constant over a range of production but can change when production exceeds certain levels.

Inflationary Price Increase

A rise in prices across the board that is often attributed to an increase in the money supply or demand outpacing supply.

Absorption Costing

An accounting method that includes all manufacturing costs (direct materials, direct labor, and both variable and fixed overhead) in the cost of a product.