Ch. R - Review of Basic Concepts
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- Multiply or divide as indicated. Write answers in lowest terms as needed. (4/5)*(6/7)
Problem 25
- Use set notation, and list all the elements of each set. {x | x is a natural number greater than 8 and less than 15}
Problem 25
- Factor out the greatest common factor from each polynomial. See Example 1. 2(m-1)-3(m-1)^2+2(m-1)^3
Problem 25
Problem 25a
Write each rational expression in lowest terms. 8k + 16 / 9k + 18
- Multiply or divide as indicated. Write answers in lowest terms as needed. (5/9)*(2/7)
Problem 26
- Use set notation, and list all the elements of each set. {x | x is a natural number not greater than 4}
Problem 26
- Add or subtract, as indicated. See Example 2. 3(8p^2-5p) - 5(3p^2-2p+4)
Problem 26
- Factor out the greatest common factor from each polynomial. See Example 1. 5(a+3)^3-2(a+3)+(a+3)^2
Problem 26
Problem 26
Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. (-2x5)5
- If the expression is in exponential form, write it in radical form and evaluate if possible. If it is in radical form, write it in exponential form. Assume all variables represent posi-tive real numbers. -5z^2/3
Problem 26
- Insert ∈ or ∉ in each blank to make the resulting statement true. 6 _____ {3, 4, 5, 6}
Problem 27
- Find each sum or difference. -6 + (-13)
Problem 27
- Concept Check When directed to completely factor the polynomial 4x^2y^5-8xy^3,a student wrote 2xy^3(2xy^2-4). When the teacher did not give him full credit, he complained because when his answer is multiplied out, the result is the original polynomial. Give the correct answer.
Problem 27
Problem 27a
Write each rational expression in lowest terms. m2 - 4m + 4 / m2 + m - 6
Problem 28
Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. -(2x0y4)3
- Multiply or divide as indicated. Write answers in lowest terms as needed. (3/20)*(5/21)
Problem 28
- Add or subtract, as indicated. See Example 2. -(8x^3+x-3) + (2x^3+x^2) - (4x^2+3x-1)
Problem 28
- Concept Check Kurt factored 16a^2-40a-6a+15 by grouping and obtained (8a-3)(2a-5). Callie factored the same polynomial and gave an answer of (3-8a)(5-2a). Which answer is correct?
Problem 28
- If the expression is in exponential form, write it in radical form and evaluate if possible. If it is in radical form, write it in exponential form. Assume all variables represent posi-tive real numbers. p^5/4
Problem 28
- Insert ∈ or ∉ in each blank to make the resulting statement true. 5 ____ {4, 6, 8, 10}
Problem 29
- Find each sum or difference. -15+6
Problem 29
- Find each product. See Examples 3–5. (14r-1)(17r+2)
Problem 29
Problem 29a
Write each rational expression in lowest terms. 8m2 + 6m - 9 / 16m2 - 9
- Multiply or divide as indicated. Write answers in lowest terms as needed. (1/8)*(10/7)
Problem 30
- Insert ∈ or ∉ in each blank to make the resulting statement true. 13 _____ {3, 5, 12, 14}
Problem 30
- Find each product. See Examples 3–5. (5m-6)(3m+4)
Problem 30
- Factor each polynomial by grouping. See Example 2. 10ab-6b+35a-21
Problem 30
Problem 30
Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. (p4/q)2
- If the expression is in exponential form, write it in radical form and evaluate if possible. If it is in radical form, write it in exponential form. Assume all variables represent posi-tive real numbers. (5r + 3t)^4/7
Problem 30
- Insert ∈ or ∉ in each blank to make the resulting statement true. 0 _____ {0, 2, 3, 4}
Problem 31