Solve the Polynomial Inequality and Graph the Solution Set on a Number

question 468

Multiple Choice

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval
notation.
- $$16 x ^ { 3 } + 48 x ^ { 2 } - 25 x - 75 > 0$$

• A) \(\left( - 3 , - \frac { 5 } { 4 } \right) \cup \left( \frac { 5 } { 4 } , \infty \right)\)
• B) \(\left( \frac { 5 } { 4 } , \infty \right)\)
• C) \(( - \infty , - 3 ) \cup \left( - \frac { 5 } { 4 } , \frac { 5 } { 4 } \right)\)
• D) \(( - \infty , - 3 ] \cup \left[ - \frac { 5 } { 4 } , \frac { 5 } { 4 } \right]\)

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Definitions:

Dummy Variables

In statistical modeling, these are artificial variables created to represent an attribute with two or more distinct categories or levels.

Regression Analysis

A statistical method used to explore the relationship between a dependent variable and one or more independent variables.

Sum Of Squares

A statistical technique used to measure the dispersion or variation within a data set by squaring the differences from the mean and summing all the resulting squares.

Observed Errors

The discrepancies between measured values and the true values, often due to measurement limitations or external factors.