Find (A) the leading term of the polynomial, (B) the limit as \( x \) approaches \( \infty \), and (C) the limit as \( x \) approaches \( -\infty \) \( p(x)=19+3 x^{2}-6 x^{3} \) (A) The leading term is \( \square \)

The leading term of the polynomial \( p(x) = 19 + 3x^2 - 6x^3 \) is determined by the term with the highest degree. Here, the \( -6x^3 \) term has the highest degree of 3, making it the leading term. Thus, the leading term is \( -6x^3 \). As \( x \) approaches \( \infty \), the dominating term in the polynomial is again \( -6x^3 \). Since the coefficient is negative and the degree is odd, the limit will approach \( -\infty \). Therefore, the limit as \( x \) approaches \( \infty \) is \( -\infty \). Conversely, as \( x \) approaches \( -\infty \), the \( -6x^3 \) term still dominates, but because \( x \) is negative, raising it to an odd power results in a positive outcome. Hence, the overall limit as \( x \) approaches \( -\infty \) will be \( +\infty \).