When is the expression 4 x + 2 x 2 + 2 x − 15 undefined? Answer Options Elimination Tool Select one answer A x = − 1 2 B x = 1 2 C x = − 5 or x = 3 D x = − 3 or x = 5 E x = 3 or x = 5

The given expression is:

\[
4x + 2x^2 + 2x - 15
\]

This is a **polynomial**, and polynomials are defined for all real numbers. A polynomial expression like this will never be undefined because it does not involve any denominators, square roots, logarithms, or other operations that could lead to undefined values for specific values of \(x\).

Thus, the expression is defined for all real values of \(x\). Therefore, **none of the answer choices are correct** in this case because the expression is always defined.

Do you have any further questions, or would you like more details on this topic? Here are five follow-up questions to consider:

1. How do you identify when an expression is undefined?
2. What kinds of expressions can lead to undefined values?
3. How can factoring help in identifying the behavior of polynomials?
4. What role do roots or zeros of a polynomial play in solving equations?
5. How would you solve for \(x\) if the polynomial were set equal to zero?

**Tip:** Polynomials are continuous and defined for all real numbers, but fractions and square roots can introduce restrictions.

When is the expression 4x + 2x^2 + 2x − 15 undefined? Answer Options Elimination Tool Select one answer A: x = −1/2, B: x = 1/2, C: x = −5 or x = 3, D: x = −3 or x = 5, E: x = 3 or x = 5

Explore why the polynomial expression 4x + 2x^2 + 2x - 15 is defined for all real numbers. Learn about the behavior of polynomials, how to identify when expressions are undefined, and how this applies to algebraic concepts. Suitable for Grades 9-12.

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