Use Synthetic Division $$f ( x ) \text { by } x - k \text { for the given value of } k \text {. Then express } f ( x ) \text { in the form } f ( x ) = ( x - k ) q ( x ) + r$$

question 270

Multiple Choice

Use synthetic division $$f ( x ) \text { by } x - k \text { for the given value of } k \text {. Then express } f ( x ) \text { in the form } f ( x ) = ( x - k ) q ( x ) + r$$ for the given value of k.
- $f ( x ) = 2 x ^ { 3 } - 3 x ^ { 2 } - 5 x + 4 ; \quad k = 2$

• A) \(f ( x ) = ( x - 2 ) \left( 2 x ^ { 2 } + 7 x + 9 \right) + 22\)
• B) \(f ( x ) = ( x - 2 ) \left( 2 x ^ { 2 } + x - 3 \right) - 2\)
• C) \(f ( x ) = ( x + 2 ) \left( 2 x ^ { 2 } + x + 3 \right) + 10\)
• D) \(f ( x ) = ( x - 2 ) \left( 2 x ^ { 2 } - 7 x + 11 \right) + 18\)

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Definitions:

Correlation Coefficient

A statistical measure that calculates the strength between two variables and their level of association, ranging from -1 to 1.

Sample Correlation Coefficient

A measure that quantifies the degree to which two variables change together, indicating the strength and direction of their linear relationship in a sample.

Test Statistic Value

A quantity derived from sample data and used in a hypothesis test to determine whether to reject the null hypothesis.

T-Table Values

Values found in a T-table are used to determine critical values of the t-distribution, helpful in hypothesis testing and constructing confidence intervals when the population standard deviation is unknown.