Determine the leading term, the leading coefficient, and the degree of the polynomial. Then classify the polynomial as constant, linear, quadratic, cubic, or quartic. \( h(x)=-6 x+5 x^{2}+x^{3} \)

The leading term of the polynomial \( h(x) = -6x + 5x^{2} + x^{3} \) is \( x^{3} \). This is because it has the highest exponent among the terms. The leading coefficient, which is the coefficient of that leading term, is \( 1 \). The degree of the polynomial is determined by the highest exponent present, which here is \( 3 \). Thus, this polynomial is classified as cubic. Fun fact: Cubic polynomials can have up to three real roots, which means they can wiggle and turn in interesting ways, unlike their simpler linear and quadratic counterparts! So, when you graph it, expect some twists and turns!