\begin{tabular}{l} What is \( (a \cdot p)(x) \) ? \\ \( \qquad p(x)=-2 x^{2} \) \\ \( p(x)=x^{2}+5 x-6 \) \\ Write your answer as a polynomial or a rational function in simplest form. \\ \hline 2 \end{tabular}

To find \( (a \cdot p)(x) \), we first need to clarify the expression. It seems there is a misunderstanding in the provided information, as \( p(x) \) is defined twice with different expressions. Let's assume you meant to find \( a \cdot p(x) \) for both definitions of \( p(x) \). We will denote the two different polynomials as follows: 1. \( p_1(x) = -2x^2 \) 2. \( p_2(x) = x^2 + 5x - 6 \) Now, we will express \( (a \cdot p_1)(x) \) and \( (a \cdot p_2)(x) \). ### Step 1: Calculate \( (a \cdot p_1)(x) \) Using the first polynomial: \[ (a \cdot p_1)(x) = a \cdot (-2x^2) = -2ax^2 \] ### Step 2: Calculate \( (a \cdot p_2)(x) \) Using the second polynomial: \[ (a \cdot p_2)(x) = a \cdot (x^2 + 5x - 6) = ax^2 + 5ax - 6a \] ### Final Answer Thus, the results are: 1. For \( p_1(x) \): \[ (a \cdot p_1)(x) = -2ax^2 \] 2. For \( p_2(x) \): \[ (a \cdot p_2)(x) = ax^2 + 5ax - 6a \] These are the polynomial expressions in simplest form for both cases. If you have a specific value for \( a \), you can substitute it into these expressions to get numerical results.