For the Polynomial, List Each Real Zero and Its Multiplicity $$f ( x ) = \left( x + \frac { 1 } { 4 } \right) ^ { 4 } ( x + 1 ) ^ { 5 }$$

question 203

Multiple Choice

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.
- $$f ( x ) = \left( x + \frac { 1 } { 4 } \right) ^ { 4 } ( x + 1 ) ^ { 5 }$$

• A) \(\frac { 1 } { 4 }\), multiplicity 4 , touches \(x\)-axis; 1 , multiplicity 5 , crosses \(x\)-axis
• B) \(\frac { 1 } { 4 }\), multiplicity 4 , crosses \(x\)-axis; 1 , multiplicity 5 , touches \(x\)-axis
• C) \(- \frac { 1 } { 4 }\), multiplicity 4 , touches \(x\)-axis; \(- 1\), multiplicity 5 , crosses \(x\)-axis
• D) \(- \frac { 1 } { 4 }\), multiplicity 4 , crosses \(x\)-axis; \(- 1\), multiplicity 5 , touches \(x\)-axis

---

Definitions:

Interval Variables

Interval variables are a type of quantitative variable that have ordered values with consistent differences but no true zero point, such as temperature in Celsius.

T-Table Values

Values in a table that represent critical values of the t-distribution used in hypothesis testing, dependent on the desired significance level and degrees of freedom.

Expected Value

The weighted average of all possible values that a random variable can take on, with the weights being the probabilities of each outcome.

Simple Linear Regression

A method for modeling the relationship between a single independent variable and a dependent variable by fitting a linear equation to observed data.