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Polynomials

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) à· (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?

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