Assignment 5

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RESPONSE --> 8 ( 4 x^3 - 3 x^2 - 1 ) - 6 ( 4 x^3 + 8 x - 2 ) 32x^3 - 24x^2 - 8 - 24x^3 - 48x + 12 8x^3 - 24x^2 - 48x + 4

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14:42:31 ** 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 8úx^3 - 24úx^2 - 48úx + 4 **

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RESPONSE --> ok

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14:45:55 Query 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

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14:46:04 ** 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 --> ok

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14:48:34 Query 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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RESPONSE --> (x - 1) ( x + 1) x(x+1) - 1(x+1) x^2 + 1x - 1x - 1 x^2 - 1

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14:48:45 ** 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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RESPONSE --> ok

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14:58:36 Query 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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RESPONSE --> (2x + 3y)^2 (2x + 3y) (2x + 3y) 2x^2 + 2 * 2x * 3y + 3y^2 2x^2 + 12xy + 3y^2

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14:58:52 ** 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. **

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RESPONSE --> ok

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15:22:50 Query R.4.90 (was R.5.102). Explain why the degree of the product of two polynomials equals the sum of their degrees.

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RESPONSE --> I know its by using the law of exponents and distributive law but i just cant explain how.

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15:23:40 ** 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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RESPONSE --> understand

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15:23:48 Query Add comments on any surprises or insights you experienced as a result of this assignment.

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RESPONSE --> none

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This looks good. Let me know if you have questions.