Subjects algebra

Polynomial Degree Constant

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Polynomial Degree Constant


1. The problem asks which statement is true about the polynomial function given its graph. 2. The graph has two real zeros at approximately $x = -2$ and $x = 2$. 3. The graph has turning points near $x = -1$ and $x = 1$ where it stays above the $x$-axis. 4. The polynomial values increase steeply as $x$ moves to large positive and negative values. 5. This shape and number of turning points suggest the degree of the polynomial is even, likely 4 (quartic), since even-degree polynomials typically have end behavior going to $+\infty$ or $-\infty$ on both ends. 6. The polynomial passes through the $y$-axis at the constant term, which appears to be near $y = 1$, an odd number. 7. Therefore, statement A (degree even) and D (constant term odd) are plausible. 8. Since only one option can be true, the best choice is D because the constant term is visibly odd ($\approx 1$), whereas the degree being even is general but less precise here. Final answer: **D. The constant term of the polynomial is odd.**