Download WEEK 2 DISCUSSION QUESTIONS Week 2 DQ questions 1. What

WEEK 2 DISCUSSION QUESTIONS
Week 2 DQ questions
1. What is a common factor? Where do you use the common factor in an
expression consisting of various terms? Examples??
2. Find a math website that may be of benefit to a student taking MTH209 and
write newspaper-style review of the site. Evaluate the site for its usefulness
for a student in need of some extra help, so look at usefulness, reliability,
ease of use, etc.
3. Your friend is taking an algebra class that began one week after ours.
Explain to your friend a general strategy for factoring in a very organized way.
Post an email to your friend in the appropriate discussion question thread.
4. Some people say that the Difference of Two Squares formula helps them
to multiply large numbers without using a calculator. How would you use this
formula to multiply 201 by 199? Find at least one more pair of numbers that
can be multiplied this way.
5. Choose three integers a, b, and c. (Negative numbers are welcome.) Now
use a, b, and c to create a trinomial ax2+bx+c. Can you factor this trinomial?
How would you create a trinomial that will factor?
6. (REQUIRED) Demonstrate a problem from the individual assignment showing
or explaining all aspects of the solution. Please remember to clearly identify
the section and problem number you are presenting. Also, please do not
demonstrate a problem another student has submitted.
a.
b.
c.
d.
e.
f.
Section 5.1: Exercises 40, 68, and 72
Section 5.2: Exercises 16, 62, and 80
Section 5.3: Exercises 58, 64, and 102
Section 5.4: Exercises 18, 26, 38, and 88
Section 5.5: Exercises 36, 44, 66, 72, and 82
Section 5.6: Exercises 18, 32, 54, 58, 66, 98, 100, and 104
What is a common factor? Where do you use the common factor in an expression consisting of
various terms? Examples??
In the first place, factors are terms multiplied together, and because of inverses this can be extended to
division.
You are frequently asked to find a common factor since this can be used to simplify a fraction of
equation.
For instance:
A * B * C * D = D^2 * B * C
That is equal relation to:
A = D (after dividing both sides by B * C * D)
(A * B * C)
--------------(B * C * D)
is equal to: (A / D) That's a lot easier to understand.
The factors can get a lot hairier when you begin to involve polynomials and other expressions, but it still
basically boils down to something common that is multiplied or divided as above and removing that
common part.
b. Choose three integers a, b, and c. (Negative numbers are welcome.) Now use a, b, and c
to create a trinomial ax2+bx+c. Can you factor this trinomial? How would you create a
trinomial that will factor?
Solution: let a = 3
b = -5
c = -2
3x2 – 5x - 2
3x2 – 3x -2x -2
3x (x-1) -2(x-1)
(3x -2)(x-1)
ANS
c. Your friend is taking an algebra class that started one week after ours. Describe to your
friend a general plan for factoring in a very organized method. Post an email to your friend
in the appropriate discussion question thread.
Solution:
1. Arrange all the terms in the order (from higher to lower power)
3x2 – 5x - 2
2. Break the middle term (coefficient of x) in such a way that it is the sum of that term as well
the multiplication of the two terms is same as that of the multiplication of the coefficient of the
(x2 term and constant)
3x2 – 3x -2x -2
3. Now we have four terms
3x2 – 3x -2x -2
4. Take out the common factor from first two term and common factor from the last two terms
3x (x-1) -2(x-1)
5 You will find some common term take it out
(3x -2)(x-1)
6 You will get the factors
2. Find a math website that may be of benefit to a student taking MTH209 and write newspaper-style
review of the site. Evaluate the site for its usefulness for a student in need of some additional help, so
look at usefulness, reliability, ease of use, etc.
Solutions:
There are various sites helping in mat 209 like algebrahelp.com or jiksha.com
Both of these sites are very easy to use one can easily upload the doubts three and these doubts are
solved mostly within 3-4 hrs of time, but sometimes even they are not solved. Also these sites are
reliable because I think they scrutinize the work before someone uploads a work.
4. Some people say that the Difference of Two Squares formula helps them to multiply large
numbers without using a calculator. How would you use this formula to multiply 201 by 199?
Find at least one more pair of numbers that can be multiplied this way.
Solution:
Yes difference of square can be easily used here
Take the two number be x and y
X+y = 201
x-y = 199
2x=400
X = 200
Y=1
Therefore now using square difference formula
(200-1)(200+1)
Or
2002 - 12
40000-1
39999 (ans)
6. (REQUIRED) Demonstrate a problem from the individual assignment showing or explaining all aspects
of the solution. Please remember to clearly identify the section and problem number you are
presenting. Also, please do not demonstrate a problem another student has submitted.
Solution:
21x 2  2 x  3
multiplying the coefficient of x 2 and cons tan t
ac  21* 3  63
now we try to factorize it in such a way that sum is  2
ac  9* 7
 9*7
sum  2
2
21* 3
 21*3
18
we get the two numbers as 9 and  7
therefore 9* 7
21x 2  9 x  7 x  3
nowtake the common factor out
3 x(7 x  3)  1(7 x  3)
on factorizing we get
(3 x  1)(7 x  3)
 18