In the next few slides, we will discuss
factoring and solving polynomials. Our
focus will be on the following polynomial,
found on page 396 of our text. Specifically,
this is problem #62.
3 z 3 6 z 2 27 z 54
Begin by Grouping
3 z 3 6 z 2 27 z 54
Since thi

When we are graphing these equations, we can know many of the characteristics ahead of time using
the equation.
What is the vertex? How can we find it? Is it a minimum or is it a maximum?
According to Rockswold & Krieger, The vertex is the lowest point on

Week 6 DQ1 Page 659, Math Problem #36
I solved this problem using the Product Rule for Rational Expressions. The Product Rule works
nicely for this problem because the index is the same for each expression.
n
a n b n a b
3
93 3
3
(9)(3) Multiply the expre

DQ#2 response this coming week, use #43 on page 403
x 2 25
ax 2 bx c 0
x 2 25 25 25
x 2 25 0
x
b b 2 4ac
2a
0 (0) 2 4(1)( 25)
x
2(1)
x
0 (0 0) 4(1)( 25)
2(1)
0 (0) 4( 25 )
x
2(1)
0 (0) 4 25
x
2(1)
x
0 0 100
2(1)
Formula
Subtract 25 from both sides t

1
x
x 1 x 1
x
1
x 1 x 1
Since x is on the right side, move it to the left side
Since both expressions have the same denominator, the numerators must be
equal so multiply the numerators by (-1).
x 1 1 1
x 1
1
( 1)
1 1 1 1
1 1
0 0
It looks like this eq

3x 12 x Problem #51 on page 660
3x 12 x Put both expressions under the radicand and Multiply.
36 x 2
Put solution from multiplication under the radicand.
6x 6x
Factor the term under the radicand and find the perfect roots. Take 6x, in this case, from
unde

1
2
x 1 x 2
Problem #71, on page 496.
Since each side of the equals sign contains a rational expression, I used the formula of
A C
B D Which is equivalent to
A D B C
1 ( x 2) 2 ( x 1)
x 2 2 x 1
A*D = B*C
x 2 2 x 2
x 2 2 2 x 2 2
x 2 x 4
Since (-2) does not

Week Four DQ#2
We discussed GCF, LCD and LCM in Week 2. Remember that the LCD and the LCM are the same.
Now we will use the LCM, a lot, to simplify our work with rational expressions. Find the steps that the
text lays out for finding the LCM in Chapter 7.

1
2
x
2
x 3 x 3 x 9
The lowest common multiple in this equation is: (x+3)(x-3), so then I need all the denominators to be
(x+3)(x-3).
1
2
x
2
x 3 x 3 x 9
1
2
x
2
x 3 x 3 x 9
1
2
x
2
x 3 x 3 x 9
1
2
x
2
x 3 x 3 x 9
1
2
x
2
x 3 x 3 x 9
1
2
x
2
x 3 x

One concept we will have to be aware of with rational expressions and equations is when that
expression or equation becomes undefined.
The concept of 'undefined' in math is not limited to rational expressions or equations. In fact we see it
as an issue mu

One concept we will have to be aware of with rational expressions and equations is when that
expression or equation becomes undefined.
The concept of 'undefined' in math is not limited to rational expressions or equations. In fact we see it
as an issue mu

Research the Internet to investigate the history and applications of polynomials and their factors. Using
what you learned from the Internet, why do you think polynomials are important?
http:/ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=533137&url=http%

Four methods used to solve quadratic equations, include: factoring, using the square root
formula, completing the square, and using the quadratic formula. Each method contains its own
formula for solving quadratic equations, according to the contents of t

When we are graphing these equations, we can know many of the characteristics ahead of time using
the equation.
What is the vertex? How can we find it? Is it a minimum or is it a maximum?
According to Rockswold & Krieger, The vertex is the lowest point on

DQ#2 response this coming week, use #43 on page 403
Formula
x 2 25
Subtract 25 from both sides to get the equation on the
left side.
ax 2 bx c 0
Result
x 2 25 25 25
Solve using the quadratic formula to find the solution.
Use the Standard Form for this equ

1
2
x 1 x 2
Problem #71, on page 496.
Since each side of the equals sign contains a rational expression, I used the formula of
A C
B
D
Which is equivalent to
A D B C
A*D = B*C
1 ( x 2) 2 ( x 1)
x 2 2 x 1
x 2 2 x 2
Since (-2) does not contain a variable, I

One concept we will have to be aware of with rational expressions and equations is when that
expression or equation becomes undefined.
The concept of 'undefined' in math is not limited to rational expressions or equations. In fact we see it
as an issue mu

AlgebraHelp.com. (2011). Retrieved from
http:/www.algebrahelp.com/lessons/simplifying/foilmethod/pg3.htm
FOIL Method
The FOIL Method cannot always be used to multiply two sets of parentheses. This is the case with the
problem below.
Since the second set o

1
1
x
x 1
x
x
x
1
0
x
1
1
1
1 1
x
x 1
1
1
1
1
(
1
)
1 1
Since x is on
the right side, move it
to the left side
1
0
Since both expressions have the same denominator, the numerators must be
equal so multiply the numerators by (-1).
It looks like this equat

MAT117 WEEK 3 DQ1
Research the Internet to investigate the history and applications of
polynomials and their factors. Using what you learned from the Internet,
why do you think polynomials are important?
This weeks DQ was very close to my heart, literally

Do you always use the property of distribution when multiplying monomials and polynomials? Explain
why or why not. In what situations would distribution become important?
When multiplying monomials and polynomials, the commutative property of
multiplicati

What is the relationship between exponents and logarithms?
How would you distinguish between the two, using both a graph and a sequence?
According to our text, Logarithms are inverses of exponentials. I liked the example in
this weeks reading about going

Four methods used to solve quadratic equations, include: factoring, using the square root
formula, completing the square, and using the quadratic formula. Each method contains its own
formula for solving quadratic equations, according to the contents of t

If I was teaching a relative of middle school age how to multiply polynomials, I would
first evaluate and review her homework to see what level of Algebra she was being
taught in school. I would use her textbook to review current assignments and then ask

Week 6 DQ1 Page 659, Math Problem #36
I solved this problem using the Product Rule for Rational Expressions. The Product Rule works
nicely for this problem because the index is the same for each expression.
n
a n b n a b
3
93 3
3
(9)(3)
3
27
Problem #36
M

We start needing to handle GCF's this week but right on its heels will be
LCD's and LCM's.
First, let me go over the correct vocabulary terms for the GCF, LCD, and LCM.
GCF stands for Greatest Common Factor; LCD stands for Lowest Common
Denominator; and L

4(x-3y)(x+3y)
4(x x + x 3y - 3y x - 3y 3y)
Multiply (First)
x x = x
4(x + x 3y 3y x 3y 3y)
Multiply (Outside) x 3y =
3xy
4(x + 3xy 3y x 3y 3y)
Multiply (Inside)
-3y x =
-3xy
4(x + 3xy 3xy 3y 3y)
Multiply (Last) -3y 3y = -9y
Now put these terms inside the

3xy + 24xy + 48y
Actually, the GCF is only '3y', not 3y(x+8x+16)
I will put the steps for my classmates, since I seem to be losing points left
and rightLOL
First, factor out 3y from every term in the equation:
3xy = 3y(x)
3y(x) + 24xy + 48y
24xy = 3y(8x)

64 x - 25y (Example on page 384)
This problem was factored using the difference of two squares using the
formula below:
a - b = (a - b)(a + b)
Since both terms are perfect squares, then I need to find the value for a
and for b.
a = 64 x , since the square