2/13 3.03 Overview of Polynomials - M Which polynomial is written in standard form? \( 12 p^{4}+2 p-\frac{1}{2} p^{3}-8 p^{2} \) \( 12 p^{4}+2 p-8 p^{2}-\frac{1}{2} p \) \( 12 p^{4}-\frac{1}{2} p^{3}-8 p^{2}+2 p \)

To determine which polynomial is written in standard form, we look for the polynomial where the terms are arranged in descending order of their degrees. In this case, the correct polynomial written in standard form is \( 12 p^{4}-\frac{1}{2} p^{3}-8 p^{2}+2 p \) since the term \( 12 p^4 \) has the highest degree of 4, followed by \( -\frac{1}{2} p^3 \) (degree 3), \( -8 p^2 \) (degree 2), and finally \( +2 p \) (degree 1). Standard form of a polynomial is important for simplifying operations like addition, subtraction, and multiplication. By arranging the polynomial terms in descending order, it becomes easier to combine like terms and apply various polynomial long division processes. Additionally, when graphing the polynomial, having the standard form helps determine the end behavior and key features such as intercepts more effectively!