A.Find p(x) + 3q(x)
p(x) = 2x^4 + 15x^3 - 10x^2 + 14
q(x) = 35x^4 - 16x^2 + x - 11
c.Simplify: (-3x + 4x^2 + 6x^3) - (4 - x + 2x^3) - (-6x^2 + y)
d.Add: (10x^2 + 3y^2 - 6z^2 + xy + 4yz + 2xz) + (2x^2 - y^2 + 5z^2 - 2xy + 7yz - 3xz)
e.Multiply: (2x - 3y)^2
f.Multiply: (6x - 7) (6x + 7)
g.Divide: (3x^3 - x^2 + 10x - 4) ÷ (x + 3)
B. Factor completely:
a.x^2 - 5x - 7x + 35
b.2x^2 + 11x + 5
c.x^4y - 16y
C. Solve the following problems involving applications of polynomials.
a. A photo is 4 inches longer than it is wide. A 3-inch border is placed around the photo making the total area of the photo and border 165 square inches. What are the dimensions of the photo?
b. A rectangular patio is 7 ft longer than it is wide. Determine the dimensions of the patio if it measures 13 ft diagonally.
Step by step solutions to all the problems are provided.