Assign 4  5

course Mth 158

9-22-09 5:02 p.m.I had a lot of anxiety with some of this assignment. I have been reading this book over and over and some of it I just can't grasp. I have spoken with my tutor and she is going to go over alot of it with me on Wednesday. I am also looking into getting extra time with a tutor if one is available.

" "If your solution to stated problem does not match the given solution, you should self-critique per instructions at http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm.

Your solution, attempt at solution:

If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

005. `* 4

* R.4.36 (was R.5.30). What is the single polynomial that is equal to 8 ( 4 x^3 - 3 x^2 - 1 ) - 6 ( 4 x^3 + 8 x - 2 )?

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Your solution:

8(4x^3 – 3x^2 – 1) – 6(4x^3 + 8x – 2) Here you use the distributive law (I worked it on paper and had to put it in vertical position to see it correctly.

32x^3 – 24x^2 – 8

-24x^3 +12 – 48x After distributing, I then subtracted to get

8x^3 – 24x^2 + 4 -48x

confidence rating: 3

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Given Solution:

* * ** ERRONEOUS STUDENT SOLUTION: To make this problem into a single polynomial, you can group like terms together. (8-6)+ (4x^3-4x^3) + (-3x^2) + (8x) + (-1+2).

Then solve from what you just grouped...2 (-3x^2+8x+1).

INSTRUCTOR CORRECTION:

8 is multiplied by the first polynomial and 6 by the second. You need to follow the order of operations.

Starting with

8 ( 4 x^3 - 3 x^2 - 1 ) - 6 ( 4 x^3 + 8 x - 2 ) use the Distributive Law to get

32 x^3 - 24 x^2 - 8 - 24 x^3 - 48 x + 12. Then add like terms to get

8x^3 - 24x^2 - 48x + 4 **

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Self-critique (if necessary):

Because I worked mine in vertical position, my answer was arranged differently, but still means the same (I think?)

Would it still mean the same?

The meaning is the same. However the standard form lists the terms in decreasing powers of x. Get in the habit of using this standard form because it will simplify your notation and make life easier for you.

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Self-critique Rating: 3

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Question:

* R.4.60 (was R.5.54). What is the product (-2x - 3) ( 3 - x)?

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Your solution:

(-2x – 3) ( 3 – x) Using the distributive law

-2(3) -2(-x) -3(3) -3(-x)

-6x + 2x^2 – 9 + 3x you then add like terms

-6x + 3x +2x^2 – 9

-3x + 2x^2 - 9

confidence rating: 3

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Given Solution:

* * ** Many students like to use FOIL but it's much better to use the Distributive Law, which will later be applied to longer and more complicated expressions where FOIL does not help a bit.

Starting with

(-2x - 3) ( 3 - x) apply the Distributive Law to get

-2x ( 3 - x) - 3 ( 3 - x). Then apply the Distributive Law again to get

-2x(3) - 2x(-x) - 3 * 3 - 3 ( -x) and simiplify to get

-6x + 2 x^2 - 9 + 3x. Add like terms to get

2 x^2 - 3 x - 9. **

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Self-critique (if necessary):

The answer is arranged differently because I use the vertical method to add like terms on paper, so when I transfer it to use the typewritten notations, it ends up different. I don’t think there are any discrepancies between the two.

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Self-critique Rating: 3

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Question:

* R.4.66 (was R.5.60). What is the product (x - 1) ( x + 1) and how did you obtain your result using a special product formula?

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Your solution:

Using the special formula (x-5) (x+5) = x^2 – 5^2 = x^2 – 25

We then solve for (x-1) (x+1) = x^2 – 1^2 = x^2 - 1

confidence rating: 3

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Given Solution:

Starting with

(x-1)(x+1) use the Distributive Law once to get

x ( x + 1) - 1 ( x+1) then use the Distributive Law again to get

x*x + x * 1 - 1 * x - 1 * 1. Simplify to get

x^2 +- x - x + - 1. Add like terms to get

x^2 - 1. **

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Self-critique (if necessary):

I didn’t use the distributive law first. I just followed the example in the book to get the same results, but I think if the problem were more complicated I would have to use the distributive law before I could solve.

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Self-critique Rating: 3

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Question:

* R.4.84 (was R.5.78). What is (2x + 3y)^2 and how did you obtain your result using a special product formula?

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Your solution:

I know the book shows the special formula as:

(x + a)^2 = x^2 + 2ax + a^2

x=2x and a=3y we would substitute in the right

(x + a)^2 = 2x^2 + 2 * 3y * 2x + 3y^2

I have tried several different ways to get the right answer, and none of them work. I really don’t understand this special formula at all.

confidence rating: 0

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Given Solution:

* * ** The Special Product is

• (a + b)^2 = a^2 + 2 a b + b^2.

Letting a = 2x and b = 3y we substitute into the right-hand side a^2 + 2 a b + b^2 to get

(2x)^2 + 2 * (2x) * (3y) + (3y)^2, which we expand to get

4 x^2 + 12 x y + 9 y^2. **

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Self-critique (if necessary):

I see what you have done here, but always get confused when a ( ) is used in exponents such as:

(2x)^2 Here it appears to be (2 * 2 x)^2 to get 4x^2, but when I look at it I think of it this way:

(2x)^2 = (2 * 2 x) ^2 = 4x It always seems that if you perform the 2 * 2 then the exponent would have already taken place, therefore dropping the exponent and then adding the x. The same for the last (3y)^2

It is not correct to say that a^2 = 2x^2, becuase 2x^2 means to multiply 2 by x^2 (order of operations; the square doesn't apply to the coefficient 2).

You would not write (2x)^2 as (2 * 2x)^2. Since 2 * 2x is different than 2x, these are different quantities.

It is also not correct that (2 * 2x)^2 = 4 x. Using the laws of exponents, the expression would become

(2 * 2x)^2 = 2^2 * (2x)^2 = 2^2 * 2^2 * x^2 = 4 * 4 * x^2 = 16.

Here is the correct interpretation:

a^2 is the square of a, whatever a is. It's not the square of one part of a or the other, it's the square of the whole thing.

So if a = 2x, the square of a is the square of 2x. The square of 2x is 2x * 2x, which is 4 x^2.

In symbols, if a = 2x then a^2 = (2x)^2. By the laws of exponents (2x)^2 = 2^2 * x^2 = 4 x^2.

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Self-critique Rating: 3

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Question:

* R.4.105 \ 90 (was R.5.102). Explain why the degree of the product of two polynomials equals the sum of their degrees.

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Your solution:

I am having difficulty with this chapter. I have read and studied it all day and still have trouble understanding the meaning.

The only answer I can come up with here is that when you have different degrees, you would have to add or subtract them to get a final degree.

That's pretty much it.

That answer is probably not right. I don’t know if reading the chapter again would do me any good without someone to explain it in the simplest form.

confidence rating: 0

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Given Solution:

* * ** STUDENT ANSWER AND INSTRUCTOR COMMENTS: The degree of the product of two polynomials equals the sum of their degrees because you use the law of exponenents and the ditributive property.

INSTRUCOTR COMMENTS: Not bad.

A more detailed explanation:

The Distributive Law ensures that you will be multiplying the highest-power term in the first polynomial by the highest-power term in the second.

Since the degree of each polynomial is the highest power present, and since the product of two powers gives you an exponent equal to the sum of those powers, the highest power in the product will be the sum of the degrees of the two polynomials.

Since the highest power present in the product is the degree of the product, the degree of the product is the sum of the degrees of the polynomials. **

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Self-critique (if necessary):

This is an area, along with the Geometry review that I need to review with my tutor.

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Self-critique Rating: 0

You're not doing badly here. See my notes to clarify a couple of points.

Keep in mind that you can only 'cram in' so much material in a day before you reach a saturation point. If you then step back from it for a couple of days, perhaps working on a different topic during that time, you subconsciously tend to sort it out so the next time you look at it, things start to fall into place.