To determine To decompose: The expression 10 x 3 − 15 x 2 − 35 x x 2 − x − 6 into partial fractions and check the answer using a graphing calculator. Explanation Procedure used: Decomposing a rational expression into partial fractions: Consider a rational expression of the form P ( x ) Q ( x ) , such that P ( x ) and Q ( x ) have no common factor other than 1 or –1. 1 If the degree of P ( x ) is greater than or equal to the degree of Q ( x ) , divide to express P ( x ) Q ( x ) as a quotient + remainder divided by divisor and follow steps (2)-(5) to decompose the resulting rational expression. 2 If the degree of P ( x ) is less than the degree of Q ( x ) , factor Q ( x ) into linear factors of the form ( p x + q ) n and/or quadratic factors of the form ( a x 2 + b x + c ) m . Any quadratic factor a x 2 + b x + c must be irreducible, which means that it cannot be factored into linear factors with rational coefficients. 3 Assign to each linear factor ( p x + q ) n the sum of n partial fractions: A 1 p x + q + A 2 ( p x + q ) 2 + ⋯ + A n ( p x + q ) n 4 Assign to each quadratic factor ( a x 2 + b x + c ) m the sum of m partial fractions: B 1 x + C 1 ( a x 2 + b x + c ) + B 2 x + C 2 ( a x 2 + b x + c ) 2 + ⋯ + B m x + C m ( a x 2 + b x + c ) m 5 Apply algebraic methods, to find the constants in the numerators of the partial fractions. Calculation: Consider the given rational expression 10 x 3 − 15 x 2 − 35 x x 2 − x − 6 . Since, the degree of the numerator is greater than the denominator therefore, use the division method to determine the partial fractions of the expression provided. Therefore, x 2 − x − 6 10 x − 5 10 x 3 − 15 x 2 − 35 x ( 10 x 3 − 10 x 2 − 60 x ) subtract _ − 5 x 2 + 25 x ( − 5 x 2 + 5 x + 30 ) subtract _ 20 x − 30 Hence, the division of the expression is as mentioned below. 10 x 3 − 15 x 2 − 35 x x 2 − x − 6 = 10 x − 5 + 20 x − 30 x 2 − x − 6 Further, 20 x − 30 x 2 − x − 6 = 20 x − 30 x 2 − 3 x + 2 x − 6 = 20 x − 30 x ( x − 3 ) + 2 ( x − 3 ) = 20 x − 30 ( x + 2 ) ( x − 3 ) Here, the degree of the numerator is less than the denominator. Hence, determine the partial fractions of the rational term 20 x − 30 ( x + 2 ) ( x − 3 )

Pearson eText Algebra and Trigonometry: Graphs and Models -- Instant Access (Pearson+)

6th Edition

ISBN: 9780136880172

Author: Marvin Bittinger, Judith Beecher

Publisher: PEARSON+

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Chapter 9.8, Problem 12E

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To decompose: The expression 10x3−15x2−35xx2−x−6 into partial fractions and check the answer using a graphing calculator.

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Chapter 9.8, Problem 11E

Chapter 9.8, Problem 13E

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5) You are purchasing a game for $30. You have a 5% off coupon and sales tax is 5%. What will your final price be? Does it matter if you take off the coupon first or add in the tax first? 6) You have ten coupons that allow you to take 10% off the sales price of a jacket, and for some strange reason, the store is going to allow you to use all ten coupons! Does this mean you get the jacket for free? Let's really think about what would happen at the checkout. First, the teller would scan the price tag on the jacket, and the computer would show the price is $100. After the teller scans the first coupon, the computer will take 10% off of $100, and show the price is $90. (Right? Think about why this is.) Then after the teller scans the second coupon, the computer will take 10% off of $90. (a) Continue this reasoning to fill in the table below showing the price of the jacket (y) after you apply x coupons. (b) Make a graph showing the price of the jacket from x = 0 to x = 10 coupons applied.…

(a) (b) (c) (d) de unique? Answer the following questions related to the linear system x + y + z = 2 x-y+z=0 2x + y 2 3 rewrite the linear system into the matrix-vector form A = 5 Fuse elementary row operation to solve this linear system. Is the solution use elementary row operation to find the inverse of A and then solve the linear system. Verify the solution is the same as (b). give the null space of matrix A and find the dimension of null space. give the column space of matrix A and find the dimension of the column space of A (Hint: use Rank-Nullity Theorem).

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Pearson eText Algebra and Trigonometry: Graphs and Models -- Instant Access (Pearson+)

Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E Ch. 9.1 - Prob. 9E Ch. 9.1 - Prob. 10E

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Golden Harvest Foods makes...Ch. 9.7 - Prob. 67E Ch. 9.7 - Prob. 68E Ch. 9.7 - Prob. 69E Ch. 9.7 - Prob. 70E Ch. 9.7 - Prob. 71E Ch. 9.7 - Prob. 72E Ch. 9.7 - Prob. 73E Ch. 9.7 - Prob. 74E Ch. 9.7 - Prob. 75E Ch. 9.7 - Prob. 76E Ch. 9.7 - Prob. 77E Ch. 9.7 - Prob. 78E Ch. 9.7 - Prob. 79E Ch. 9.7 - Prob. 80E Ch. 9.7 - Prob. 81E Ch. 9.7 - Prob. 82E Ch. 9.7 - Prob. 83E Ch. 9.7 - Prob. 84E Ch. 9.7 - Prob. 85E Ch. 9.7 - Prob. 86E Ch. 9.7 - Prob. 87E Ch. 9.7 - Prob. 88E Ch. 9.7 - Prob. 89E Ch. 9.7 - Prob. 90E Ch. 9.7 - Prob. 91E Ch. 9.8 - Prob. 1E Ch. 9.8 - Prob. 2E Ch. 9.8 - Prob. 3E Ch. 9.8 - Prob. 4E Ch. 9.8 - Prob. 5E Ch. 9.8 - Prob. 6E Ch. 9.8 - Decompose into partial fractions. Check your...Ch. 9.8 - Prob. 8E Ch. 9.8 - Prob. 9E Ch. 9.8 - Prob. 10E Ch. 9.8 - Prob. 11E Ch. 9.8 - Decompose into partial fractions. Check your...Ch. 9.8 - Prob. 13E Ch. 9.8 - Prob. 14E Ch. 9.8 - Prob. 15E Ch. 9.8 - Prob. 16E Ch. 9.8 - Prob. 17E Ch. 9.8 - Prob. 18E Ch. 9.8 - Prob. 19E Ch. 9.8 - Prob. 20E Ch. 9.8 - Prob. 21E Ch. 9.8 - Prob. 22E Ch. 9.8 - Prob. 23E Ch. 9.8 - Prob. 24E Ch. 9.8 - Prob. 25E Ch. 9.8 - Prob. 26E Ch. 9.8 - Prob. 27E Ch. 9.8 - Prob. 28E Ch. 9.8 - Prob. 29E Ch. 9.8 - Prob. 30E Ch. 9.8 - Prob. 31E Ch. 9.8 - Prob. 32E Ch. 9.8 - Prob. 33E Ch. 9.8 - Prob. 34E Ch. 9.8 - Prob. 35E Ch. 9 - Prob. 1MC Ch. 9 - Prob. 2MC Ch. 9 - Prob. 3MC Ch. 9 - Prob. 4MC Ch. 9 - Prob. 5MC Ch. 9 - Prob. 6MC Ch. 9 - Prob. 7MC Ch. 9 - Prob. 8MC Ch. 9 - Prob. 9MC Ch. 9 - Prob. 10MC Ch. 9 - Prob. 11MC Ch. 9 - Prob. 12MC Ch. 9 - Prob. 13MC Ch. 9 - Prob. 14MC Ch. 9 - Prob. 15MC Ch. 9 - Prob. 16MC Ch. 9 - Prob. 17MC Ch. 9 - Prob. 18MC Ch. 9 - Prob. 19MC Ch. 9 - Prob. 20MC Ch. 9 - Prob. 21MC Ch. 9 - Prob. 1RE Ch. 9 - Prob. 2RE Ch. 9 - Prob. 3RE Ch. 9 - Prob. 4RE Ch. 9 - Prob. 5RE Ch. 9 - Prob. 6RE Ch. 9 - Prob. 7RE Ch. 9 - Prob. 8RE Ch. 9 - Prob. 9RE Ch. 9 - Prob. 10RE Ch. 9 - Prob. 11RE Ch. 9 - Prob. 12RE Ch. 9 - Prob. 13RE Ch. 9 - Prob. 14RE Ch. 9 - Prob. 15RE Ch. 9 - Prob. 16RE Ch. 9 - Prob. 17RE Ch. 9 - Prob. 18RE Ch. 9 - Prob. 19RE Ch. 9 - Prob. 20RE Ch. 9 - Prob. 21RE Ch. 9 - Prob. 22RE Ch. 9 - Prob. 23RE Ch. 9 - Prob. 24RE Ch. 9 - Prob. 25RE Ch. 9 - Prob. 26RE Ch. 9 - Prob. 27RE Ch. 9 - Prob. 28RE Ch. 9 - Prob. 29RE Ch. 9 - Prob. 30RE Ch. 9 - Prob. 31RE Ch. 9 - Prob. 32RE Ch. 9 - Prob. 33RE Ch. 9 - Prob. 34RE Ch. 9 - Prob. 35RE Ch. 9 - Prob. 36RE Ch. 9 - Prob. 37RE Ch. 9 - Prob. 38RE Ch. 9 - Prob. 39RE Ch. 9 - Find A–1, if it exists. 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