# Fundamental operations on polynomials and factoring

A.Find p(x) + 3q(x)
p(x) = 2x^4 + 15x^3 - 10x^2 + 14
q(x) = 35x^4 - 16x^2 + x - 11

b.Find P(-1/2) if P(x) = 4x^4 -2x^3 + 17

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) รท (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.

c. Three consecutive even integers are such that the square of the third is 100 more than the square of the second. Find the three integers.

I have completed most of these but was a little confused. I had the hardest problems with the word problems.

Solution Summary

Step by step solutions to all the problems are provided.

\$2.19
• Plain text
• Cited sources when necessary
• Attached file(s)
• 259074_solution.doc

Sandhya Sharma, MSc

Rating 4.9/5

Active since 2008

BSc, Meerut University
MSc, Meerut University
MSc, AIT

Responses 1999