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About Chanda Walker
Expertise
Any high school math problems. Please don't just type in the math problem without comments. If don't tell me about the trouble you are having, I can't help.

Experience
I have tutored in these areas for years and I home school. I use algebra, calculus, and statistics extensively in my career.

Organizations
SPIE Sigma Xi

Publications
Chapter in the book "Optical Systems Design" Applied Optics

Education/Credentials
BS in mathematics; PhD Optical Science

Awards and Honors
US Patent #7,106,457

Past/Present Clients
Intel HP Kodak Compaq Duke University NASA

You are here: Experts > Science > Math for Kids > Algebra > Math

Algebra - Math

Expert: Chanda Walker - 2/28/2009

Question
Chandra

Can you help with this

B. Factor completely:
a.   x2 – 5x – 7x + 35
b.   2x2 + 11x + 5
c.   x4y – 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.

Answer
x^2 - 5x - 7x + 35

x(x - 5) - 7(x - 5)
(x-7)(x-5)

********************

2x^2 + 11x + 5
(2x + 1)(x + 5)

********************

x^4 y - 16y
y(x^4 - 16)
y(x^2 - 4)(x^2 + 4)
y(x - 2)(x + 2)(x^2 + 4)

********************

l = 4 + w
a = (l+3)(w+3) = 165

(4 + w + 3) (w + 3) = 165
(w + 7)(w + 3) = 165
w^2 + 10w + 21 - 165 = 0
w^2 + 10w - 144 = 0
(w - 8)(w + 18)
w = {-18, 8}

dimensions are rarely negative so
w = 8
l = 12

************************

l = w + 7

l^2 + w^2 = 13^2
(w + 7)^2 + w^2 = 169
2w^2 + 14w + 49 - 169 = 0
2w^2 + 14w - 120 = 0
(2w - 10)(w + 12) = 0
w = {5, -12}

w = 5
l = 12

****************

x, x+2, x+4

(x+4)^2 = 100 + (x+2)^2

x^2 + 8x + 16 = x^2 + 4x + 4 + 100
4x + 16 - 104 = 0
4x - 88 = 0
4x = 88
x = 22

The integers are 22, 24, 26.

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