The systematic elimination of extraneous variables other than those you are interested in can be achieved in:

The correct answer is experimental research.

To understand why, let us first break down what the question is asking. The key phrase here is "systematic elimination of extraneous variables other than those you are interested in." This describes a very specific and deliberate process of controlling everything that could interfere with a study's results, so that only the variable the researcher cares about is allowed to vary. Let us explore what this means and why experimental research is uniquely suited for it.

What are extraneous variables?
In any study, a researcher is typically interested in the relationship between two things: an independent variable (the cause or factor being manipulated) and a dependent variable (the outcome being measured). However, in the real world, many other factors — called extraneous variables — could also influence the dependent variable. If these are not controlled, the researcher cannot be sure whether the observed effect is truly due to the independent variable or due to something else entirely. This "something else" is also known as a confounding variable.

How does experimental research eliminate extraneous variables?
Experimental research is specifically designed with mechanisms to control or eliminate extraneous variables. These mechanisms include:

1. Random Assignment: Participants are randomly assigned to either the experimental group (which receives the treatment/manipulation) or the control group (which does not). Random assignment ensures that any pre-existing differences between participants are distributed evenly across groups by chance, effectively neutralizing those differences so they cannot skew the results.

2. Controlled Conditions: The researcher holds all other variables constant. For example, if testing whether a new drug reduces anxiety, the experimenter would ensure that both groups experience the same environment, the same time of day for testing, the same instructions, and so on — isolating the drug as the only difference.

3. Manipulation of the Independent Variable: Only the researcher deliberately changes the independent variable. Everything else is kept the same. This precise manipulation, combined with control, is what makes cause-and-effect conclusions possible.

Because of these features, experimental research is the only research method that allows researchers to establish cause-and-effect relationships with confidence.

Why the other options are incorrect:

• Qualitative research focuses on exploring subjective experiences, meanings, and phenomena through methods like interviews and observations. It does not involve controlling or eliminating extraneous variables — it embraces the complexity of the natural context.

• Correlational research examines the statistical relationship between two or more variables as they naturally exist, without any manipulation. Because the researcher does not intervene or control conditions, extraneous variables remain present and can distort conclusions. This is why correlational research can only establish association, not causation — summarized by the well-known principle: "Correlation does not imply causation."

• Longitudinal research is a method that follows the same group of participants over an extended period of time to observe changes. While it is powerful for studying development and change, it does not inherently control or eliminate extraneous variables — many uncontrolled life events can occur over the study period and act as confounds.

Summary:
Experimental research is the gold standard for controlling unwanted influences because it uniquely combines random assignment, deliberate manipulation of the independent variable, and control of all other conditions. This systematic elimination of extraneous variables is the defining feature that separates experimental research from all other research designs, and it is precisely what the question describes.