Assignment:
A. Solve the following questions involving fundamental operations on polynomials
a. Find p(x) + 4q(x) given p(x)=4x4 + 10x3 - 2x2 + 13 and q(x) = 2x4+ 5x2 - 3
b. Find P(-1/2) if P(x) = 2x4 + x3 + 12
c. Simplify: (-4 + x2 + 2x3) - (-6 - x + 3x3) - (-6y3 + y2)
d. Add: (2x2 + 6y2 + 4z2 + 3xy + yz + zx) + (4x2 + 3y2 + z2 - 3xy - 9yz + 5zx)
e. Multiply: (3x + 3y)2
f. Multiply: (3x + 4) (3x - 4)
g. Divide: (2x3 - x2 + 3x -1) ÷ (x + 2)
B. Factor completely:
a. x2 - 7x - 9x + 63
b. 4x2 + 34x + 42
c. x4 - 1
C. Solve the following problems involving applications of polynomials.
a. A photo is 3 inches longer that it is wide. A 2-inch border is placed around the photo making the total area of the photo and border 108in2. What are the dimensions of the photo?
b. A rectangular parking lot is 50 ft longer than it is wide. Determine the dimensions of the parking lot if it measures 250 ft diagonally.
c. Bob has a yard containing a garden; the rest of the yard is covered with grass. The yard is rectangular, measuring x meters long by x+2 meters wide, and the garden is square with each side measuring 6 meters. If the area of grass is 63 square meters, what are the dimensions of the yard?
Provide complete and step by step solution for the question and show calculations and use formulas.