Question
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Which of the following represents a constant from the expression given? \( 15 x^{2}+2 x+9 \) A. 15 B. 2 C. 24 D. 9

Ask by Floyd Hamilton. in the United States
Mar 09,2025

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Tutor-Verified Answer

Answer

The constant in the expression is 9.

Solution

**Step 1:** Identify the term that does not have a variable. The expression given is \[ 15x^2 + 2x + 9 \] In this expression: - \(15x^2\) is the term with \(x^2\), - \(2x\) is the term with \(x\), and - \(9\) is the term without any \(x\). **Step 2:** Recognize the constant. A constant is a term that does not change regardless of the value of \(x\). Thus, the constant is the term that does not contain \(x\). **Step 3:** Determine the constant term. Since \(9\) is the only term without \(x\), it is the constant. **Final Answer:** D. \(9\)

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The Deep Dive

In the expression \( 15 x^{2} + 2 x + 9 \), the constant term is the number that does not have a variable attached to it. In this case, that would be 9, as it remains unchanged regardless of the value of \( x \). So, the answer is D. 9! Now, for some additional knowledge! The constant term in a polynomial represents the value of the polynomial when the variable \( x \) is equal to zero. Thus, substituting \( x = 0 \) into the expression will give you the value of the polynomial solely based on the constant term. Another fun fact: The degree of a polynomial is determined by the highest power of the variable present. Here, the term \( 15 x^{2} \) dominates with a degree of 2, classifying this polynomial as a quadratic. Quadratics have various applications in physics, engineering, and finance, often modeling parabolic trajectories and optimizing systems!

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