I need help with these please, also can you kindly provide explanations?

1. Divide the following polynomials. a. Using long division: (41:4 + 5:133 + 33 1) + (232 + 1) b. Using synthetic division: (3:5 43:4 + 42:2 + 2x + 3) + (.7; 3) 2. A popular mode] of carry-on luggage has a. length that is 10 greater than its depth. Airline regulations require that the sum of the length, width, and depth is 40 inches. These conditions can be modeled by a function that gives the volume of the luggage, V, in cubic inches, in terms of its depth, x, in inches. a. Write the function V(:I:). b. If the volume of the carry on luggage is 2000in3, determine two possibilities for its depth. c. If the volume of the carry on luggage is 15003119, determine two possibilities for its depth. 3. an) = +3; 5514 {1. Determine if the function has any symmetry. b. Find all x intercepts and yintercepts. c. Find any vertical and horizontal asymptotes. :1. Find a point between and beyond each x-intercept and vertical asymptote. e. Graph the function