Assign5 R4

course Mth 158

W?????L?????W?assignment #005005. `query 5

Your work has been received. Please scroll through the document to see any inserted notes (inserted at the appropriate place in the document, in boldface) and a note at the end. The note at the end of the file will confirm that the file has been reviewed; be sure to read that note. If there is no note at the end, notify the instructor through the Submit Work form, and include the date of the posting to your access page.

College Algebra

01-21-2007

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18:44:05

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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RESPONSE -->

8(4x^3-3x^2-1)-6(4x^3+8x-2)

32x^3-24x^2-8-24x^3-48x+12

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

confidence assessment: 2

.................................................

......!!!!!!!!...................................

18:45:03

** 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 can't isolate them like that.

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

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

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RESPONSE -->

self critique assessment: 3

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18:48:20

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

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RESPONSE -->

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

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

-6x+2x^2-9+3x

2x^2-3x-9

confidence assessment: 2

.................................................

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18:48:36

** 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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RESPONSE -->

self critique assessment: 3

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18:50:57

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?

......!!!!!!!!...................................

RESPONSE -->

(x-1)(x+1) Difference of two Squares

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

x^2-1

confidence assessment: 2

.................................................

......!!!!!!!!...................................

18:51:44

** 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. **

......!!!!!!!!...................................

RESPONSE -->

So I use a different way, but got it right.

self critique assessment: 3

.................................................

......!!!!!!!!...................................

18:54:50

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

......!!!!!!!!...................................

RESPONSE -->

Distributive Property

(2x+3y)^2

(2x+3y)(2x+3y)

2x(2x+3y)+3y(2x+3y)

4x^2+6xy+6xy+9y

4x^2+12xy+9y

confidence assessment: 2

.................................................

......!!!!!!!!...................................

18:55:43

** The Special Product is

(a + b)^2 = a^2 + 2 a b + b^2.

Letting a = 2x and b = 3y we get

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

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

......!!!!!!!!...................................

RESPONSE -->

ooops forgot the y^2 but yeah I get it.

self critique assessment: 3

.................................................

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18:57:26

R.4.90 (was R.5.102). Explain why the degree of the product of two polynomials equals the sum of their degrees.

......!!!!!!!!...................................

RESPONSE -->

By the Law of Exponents

a^m*a^n=a^m+n When you multiply, you add the exponents.

confidence assessment: 2

.................................................

......!!!!!!!!...................................

18:57:45

** 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. **

......!!!!!!!!...................................

RESPONSE -->

self critique assessment: 3

.................................................

......!!!!!!!!...................................

18:58:02

Add comments on any surprises or insights you experienced as a result of this assignment.

......!!!!!!!!...................................

RESPONSE -->

confidence assessment: 3

.................................................

end of document

Good answers and/or self-critiques. Let me know if you have questions.

Assign5 R4

course Mth 158

W?????L?????W?assignment #005005. `query 5

Your work has been received. Please scroll through the document to see any inserted notes (inserted at the appropriate place in the document, in boldface) and a note at the end. The note at the end of the file will confirm that the file has been reviewed; be sure to read that note. If there is no note at the end, notify the instructor through the Submit Work form, and include the date of the posting to your access page.

College Algebra

01-21-2007

......!!!!!!!!...................................

18:44:05

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 )?

......!!!!!!!!...................................

RESPONSE -->

8(4x^3-3x^2-1)-6(4x^3+8x-2)

32x^3-24x^2-8-24x^3-48x+12

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

confidence assessment: 2

.................................................

......!!!!!!!!...................................

18:45:03

** 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 can't isolate them like that.

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

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

......!!!!!!!!...................................

RESPONSE -->

self critique assessment: 3

.................................................

......!!!!!!!!...................................

18:48:20

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

......!!!!!!!!...................................

RESPONSE -->

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

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

-6x+2x^2-9+3x

2x^2-3x-9

confidence assessment: 2

.................................................

......!!!!!!!!...................................

18:48:36

** 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. **

......!!!!!!!!...................................

RESPONSE -->

self critique assessment: 3

.................................................

......!!!!!!!!...................................

18:50:57

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?

......!!!!!!!!...................................

RESPONSE -->

(x-1)(x+1) Difference of two Squares

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

x^2-1

confidence assessment: 2

.................................................

......!!!!!!!!...................................

18:51:44

** 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. **

......!!!!!!!!...................................

RESPONSE -->

So I use a different way, but got it right.

self critique assessment: 3

.................................................

......!!!!!!!!...................................

18:54:50

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

......!!!!!!!!...................................

RESPONSE -->

Distributive Property

(2x+3y)^2

(2x+3y)(2x+3y)

2x(2x+3y)+3y(2x+3y)

4x^2+6xy+6xy+9y

4x^2+12xy+9y

confidence assessment: 2

.................................................

......!!!!!!!!...................................

18:55:43

** The Special Product is

(a + b)^2 = a^2 + 2 a b + b^2.

Letting a = 2x and b = 3y we get

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

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

......!!!!!!!!...................................

RESPONSE -->

ooops forgot the y^2 but yeah I get it.

self critique assessment: 3

.................................................

......!!!!!!!!...................................

18:57:26

R.4.90 (was R.5.102). Explain why the degree of the product of two polynomials equals the sum of their degrees.

......!!!!!!!!...................................

RESPONSE -->

By the Law of Exponents

a^m*a^n=a^m+n When you multiply, you add the exponents.

confidence assessment: 2

.................................................

......!!!!!!!!...................................

18:57:45

** 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 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. **

......!!!!!!!!...................................

RESPONSE -->

self critique assessment: 3

.................................................

......!!!!!!!!...................................

18:58:02

Add comments on any surprises or insights you experienced as a result of this assignment.

......!!!!!!!!...................................

RESPONSE -->

confidence assessment: 3

.................................................