Explanation The given expression is t 3 + 6 t 2 − 2 t − 12 . Use the distributive property and factor out the common factor from all the terms in the expression. The common factor should be largest absolute value for constants and largest exponent variables for variables. In some cases, the pairs of terms have a common binomial factor can be removed in a process. This process is called factoring by grouping. Therefore, t 3 + 6 t 2 − 2 t − 12 = t 2 ⋅ t + 6 ⋅ t 2 − 2 ⋅ t − 2 ⋅ 6

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Chapter J.14, Problem 4E

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To factor: The expression t3+6t2−2t−12 by grouping.

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Chapter J.14, Problem 3E

Chapter J.14, Problem 5E

Chapter J Solutions

EBK COLLEGE ALGEBRA

Ch. J.1 - In Exercises 1-6, consider the numbers 23, 6, 3,...Ch. J.1 - In Exercises 16, consider the numbers 23, 6, 3,...Ch. J.1 - In Exercises 16, consider the numbers 23, 6, 3,...Ch. J.1 - In exercises 16, consider the numbers 23, 6, 3,...Ch. J.1 - In Exercises 16, consider the numbers 23, 6, 3,...Ch. J.1 - In Exercises 16, consider the numbers 23, 6, 3,...Ch. J.2 - Name the property illustrated by the sentence. 1....Ch. J.2 - Name the property illustrated by the sentence. 2....Ch. J.2 - Name the property illustrated by the sentence. 3....Ch. J.2 - Prob. 4E

Ch. J.2 - Prob. 5E Ch. J.2 - Prob. 6E Ch. J.2 - Prob. 7E Ch. J.2 - Prob. 8E Ch. J.2 - Prob. 9E Ch. J.2 - Prob. 10E Ch. J.3 - Classify the inequality as true or false. 1. 9 9 Ch. J.3 - Prob. 2E Ch. J.3 - Classify the inequality as true or false. 3. 265 Ch. J.3 - Prob. 4E Ch. J.3 - Prob. 5E Ch. J.3 - Prob. 6E Ch. J.4 - Simplify. 1. |98|Ch. J.4 - Prob. 2E Ch. J.4 - Prob. 3E Ch. J.4 - Prob. 4E Ch. J.4 - Prob. 5E Ch. J.4 - Prob. 6E Ch. J.4 - Prob. 7E Ch. J.4 - Prob. 8E Ch. J.5 - Compute and simplify. 1. 8 (11)Ch. J.5 - Compute and simplify. 2. 310(13)Ch. J.5 - Prob. 3E Ch. J.5 - Prob. 4E Ch. J.5 - Prob. 5E Ch. J.5 - Prob. 6E Ch. J.5 - Prob. 7E Ch. J.5 - Prob. 8E Ch. J.5 - Prob. 9E Ch. J.5 - Prob. 10E Ch. J.5 - Prob. 11E Ch. J.5 - Compute and simplify. 12. 1223 Ch. J.5 - Prob. 13E Ch. J.5 - Prob. 14E Ch. J.5 - Prob. 15E Ch. J.6 - Write interval notation. 1. {x| 5 x 5}Ch. J.6 - Prob. 2E Ch. J.6 - Write interval notation. 3. {x | x 2}Ch. J.6 - Write interval notation. 4. {x | x 3.8}Ch. J.6 - Prob. 5E Ch. J.6 - Prob. 6E Ch. J.6 - Prob. 7E Ch. J.6 - Prob. 8E Ch. J.6 - Prob. 9E Ch. J.6 - Write interval notation for the graph. 10.Ch. J.7 - Simplify. 1. 36 Ch. J.7 - Prob. 2E Ch. J.7 - Prob. 3E Ch. J.7 - Prob. 4E Ch. J.7 - Prob. 5E Ch. J.7 - Prob. 6E Ch. J.7 - Prob. 7E Ch. J.7 - Prob. 8E Ch. J.7 - Prob. 9E Ch. J.7 - Prob. 10E Ch. J.8 - Convert to scientific notation. 1. 18,500,000 Ch. J.8 - Prob. 2E Ch. J.8 - Prob. 3E Ch. J.8 - Prob. 4E Ch. J.8 - Convert to decimal notation. 5.4.3 108 Ch. J.8 - Prob. 6E Ch. J.8 - Convert to decimal notation. 7.6.203 1011 Ch. J.8 - Prob. 8E Ch. J.9 - Calculate. 1. 3 + 18 6 3 Ch. J.9 - Calculate. 2. 5 3 + 8 32 + 4(6 2)Ch. J.9 - Calculate. 3. 5(3 8 32 + 4 6 2)Ch. J.9 - Calculate. 4. 16 4 4 2 256 Ch. J.9 - Calculate. 5. 26 23 210 28 Ch. J.9 - Calculate. 6. 4(86)243+2831+190 Ch. J.9 - Calculate. 7. 64 [(4) (2)]Ch. J.9 - Prob. 8E Ch. J.10 - Determine the degree of the polynomial. 1. 5 x6 Ch. J.10 - Prob. 2E Ch. J.10 - Prob. 3E Ch. J.10 - Prob. 4E Ch. J.10 - Prob. 5E Ch. J.10 - Prob. 6E Ch. J.10 - Prob. 7E Ch. J.10 - Prob. 8E Ch. J.11 - Add or subtract. 1. (8y 1) (3 y)Ch. J.11 - Add or subtract. 2. (3x2 2x x3 + 2) (5x2 8x ...Ch. J.11 - Prob. 3E Ch. J.11 - Prob. 4E Ch. J.11 - Prob. 5E Ch. J.12 - Prob. 1E Ch. J.12 - Prob. 2E Ch. J.12 - Prob. 3E Ch. J.12 - Prob. 4E Ch. J.12 - Prob. 5E Ch. J.12 - Prob. 6E Ch. J.13 - Multiply. 1. (x + 3)2 Ch. J.13 - Multiply. 2. (5x 3)2 Ch. J.13 - Multiply. 3. (2x + 3y)2 Ch. J.13 - Prob. 4E Ch. J.13 - Multiply. 5. (n + 6) (n 6)Ch. J.13 - Prob. 6E Ch. J.14 - Factor out the largest common factor. 1. 3x + 18 Ch. J.14 - Prob. 2E Ch. J.14 - Prob. 3E Ch. J.14 - Prob. 4E Ch. J.14 - Prob. 5E Ch. J.14 - Prob. 6E Ch. J.14 - Prob. 7E Ch. J.14 - Prob. 8E Ch. J.14 - Prob. 9E Ch. J.14 - Prob. 10E Ch. J.14 - Prob. 11E Ch. J.14 - Prob. 12E Ch. J.15 - Factor. 1. 8x2 6x 9 Ch. J.15 - Factor. 2. 10t2 + 4t 6 Ch. J.15 - Factor. 3. 18a2 51a + 15 Ch. J.16 - Factor the difference of squares. 1. z2 81 Ch. J.16 - Factor the difference of squares. 2. 16x2 9 Ch. J.16 - Factor the difference of squares. 3. 7pq4 7py4 Ch. J.16 - Factor the square of a binomial. 4. x2 + 12x + 36 Ch. J.16 - Prob. 5E Ch. J.16 - Factor the square of a binomial. 6. a3 + 24a2 +...Ch. J.16 - Factor the sum or the difference of cubes. 7. x3 +...Ch. J.16 - Factor the sum or the difference of cubes. 8. m3 ...Ch. J.16 - Prob. 9E Ch. J.16 - Prob. 10E Ch. J.17 - Prob. 1E Ch. J.17 - Prob. 2E Ch. J.17 - Prob. 3E Ch. J.17 - Prob. 4E Ch. J.17 - Solve. 5. 7y 1 = 23 5y Ch. J.17 - Prob. 6E Ch. J.17 - Prob. 7E Ch. J.17 - Solve. 8. 5y 4 (2y 10) = 25 Ch. J.18 - Prob. 1E Ch. J.18 - Prob. 2E Ch. J.18 - Prob. 3E Ch. J.18 - Prob. 4E Ch. J.18 - Prob. 5E Ch. J.18 - Prob. 6E Ch. J.19 - Prob. 1E Ch. J.19 - Prob. 2E Ch. J.19 - Prob. 3E Ch. J.19 - Prob. 4E Ch. J.19 - Prob. 5E Ch. J.19 - Prob. 6E Ch. J.19 - Prob. 7E Ch. J.19 - Prob. 8E Ch. J.20 - Prob. 1E Ch. J.20 - Prob. 2E Ch. J.20 - Prob. 3E Ch. J.20 - Prob. 4E Ch. J.20 - Prob. 5E Ch. J.20 - Prob. 6E Ch. J.21 - Prob. 1E Ch. J.21 - Prob. 2E Ch. J.21 - Prob. 3E Ch. J.21 - Prob. 4E Ch. J.21 - Prob. 5E Ch. J.21 - Prob. 6E Ch. J.22 - Prob. 1E Ch. J.22 - Prob. 2E Ch. J.22 - Prob. 3E Ch. J.22 - Prob. 4E Ch. J.22 - Prob. 5E Ch. J.22 - Prob. 6E Ch. J.23 - Prob. 1E Ch. J.23 - Prob. 2E Ch. J.23 - Prob. 3E Ch. J.23 - Prob. 4E Ch. J.23 - Prob. 5E Ch. J.23 - Prob. 6E Ch. J.24 - Simplify. 1. xyyx1y+1x Ch. J.24 - Prob. 2E Ch. J.24 - Prob. 3E Ch. J.24 - Prob. 4E Ch. J.24 - Simplify. 5. abba1a1b Note: b a = 1(a b)Ch. J.25 - Prob. 1E Ch. J.25 - Prob. 2E Ch. J.25 - Prob. 3E Ch. J.25 - Prob. 4E Ch. J.25 - Prob. 5E Ch. J.25 - Prob. 6E Ch. J.25 - Prob. 7E Ch. J.25 - Prob. 8E Ch. J.25 - Prob. 9E Ch. J.25 - Prob. 10E Ch. J.25 - Prob. 11E Ch. J.25 - Prob. 12E Ch. J.25 - Prob. 13E Ch. J.25 - Prob. 14E Ch. J.25 - Prob. 15E Ch. J.25 - Prob. 16E Ch. J.25 - Prob. 17E Ch. J.25 - Prob. 18E Ch. J.25 - Prob. 19E Ch. J.25 - Prob. 20E Ch. J.26 - Prob. 1E Ch. J.26 - Prob. 2E Ch. J.26 - Prob. 3E Ch. J.26 - Prob. 4E Ch. J.26 - Prob. 5E Ch. J.26 - Prob. 6E Ch. J.26 - Prob. 7E Ch. J.26 - Prob. 8E Ch. J.27 - Prob. 1E Ch. J.27 - Prob. 2E Ch. J.27 - Prob. 3E Ch. J.27 - Prob. 4E Ch. J.27 - Prob. 5E Ch. J.27 - Prob. 6E Ch. J.27 - Prob. 7E Ch. J.27 - Convert to exponential notation. 8. x5 Ch. J.27 - Prob. 9E Ch. J.27 - Prob. 10E Ch. J.27 - Prob. 11E Ch. J.28 - Find the length of the third side of each right...Ch. J.28 - Find the length of the third side of each right...Ch. J.28 - Find the length of the third side of each right...Ch. J.28 - Find the length of the third side of each right...Ch. J.28 - Find the length of the third side of each right...

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To factor: The expression t 3 + 6 t 2 − 2 t − 12 by grouping.

Solution Summary: The author explains how to factor the expression t3+62-2t-12 by grouping, using the distributive property and factoring out the common factor.

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To factor: The expression t3+6t2−2t−12 by grouping.

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Chapter J Solutions