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Problem 47
Find each product or quotient where possible. See Example 2. -24 -4
Problem 49
Find each product or quotient where possible. See Example 2. 100 / -25
Problem R.3.1
CONCEPT PREVIEW Fill in the blank to correctly complete each sentence. The polynomial 2x⁵ - x + 4 is a trinomial of degree _________.
Problem R.3.31
Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 2 and 3. (-4m²/tp²)⁴
Problem R.3.29
Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 2 and 3. (r⁸/s²)³
Problem R.3.9
CONCEPT PREVIEW Which of the following is the correct factorization of x⁴ - 1? A. (x² - 1) (x² + 1) B. (x² + 1) (x + 1) (x - 1) C. (x² - 1)² D. (x - 1)² (x + 1)²
Problem R.3.17
Simplify each expression. See Example 1. (-3m⁴) (6m²) (-4m⁵)
Problem R.3.15
Simplify each expression. See Example 1. 9³ • 9⁵
Problem R.3.21
Simplify each expression. See Example 1. (½ mn) (8m²n²)
Problem R.3.19
Simplify each expression. See Example 1. (5x²y) (-3x³y⁴)
Problem R.3.11
Simplify each expression. See Example 1. (-4x⁵) (4x²)
Problem R.3.7
CONCEPT PREVIEW Work each problem. Match each polynomial in Column I with its factored form in Column II. I II a. 8x³ - 27 A. (3 - 2x) (9 + 6x + 4x²) b. 8x³ + 27 B. (2x - 3) (4x² + 6x + 9) c. 27 - 8x³ C. (2x + 3) (4x² - 6x + 9)
Problem R.3.25
Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 2 and 3. (-6x²)³
Problem R.3.13
Simplify each expression. See Example 1. n⁶ • n⁴ • n
Problem R.3.35
Match each expression in Column I with its equivalent in Column II. See Example 3. I II. a. 6° A. 0 b. -6° B. 1 c. (-6)° C. -1 d. -(-6)° D. 6 E. -6
Problem R.3.23
Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 2 and 3. (2²)⁵
Problem R.3.6
CONCEPT PREVIEW Work each problem. Match each polynomial in Column I with its factored form in Column II. I II a. x² + 10xy + 25y² A. (x + 5y) (x - 5y) b. x² - 10xy + 25y² B. (x + 5y)² c. x² - 25y² C. (x - 5y)² d. 25y² - x² D. (5y + x) (5y - x)
Problem R.3.27
Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 2 and 3. -(4m³n⁰)²
Problem R.3.33
Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 2 and 3. - ( x³y⁵/z)⁰
Problem 37
Add or subtract, as indicated. See Example 4. (5x² - 4x + 7) + (-4x² + 3x - 5)
Problem 39
Add or subtract, as indicated. See Example 4. 2(12y² - 8y + 6) - 4(3y² - 4y +2)
Problem 41
Add or subtract, as indicated. See Example 4. (6m⁴ - 3m² + m) - (2m³ + 5m² + 4m) + (m² - m)
Problem 43
Find each product. See Example 5. 4x² (3x³ + 2x² - 5x +1)
Problem 45
Find each product. See Example 5. (4r - 1) (7r + 2)
Problem 47
Find each product. See Example 5. (3x + 1) (2x - 7)
Problem 49
Find each product. See Example 5. (2m + 3) (2m - 3)
Problem 51
Find each product. See Example 5. (4x² - 5y) (4x² + 5y)
Problem 53
Find each product. See Example 5. (4m + 2n)²
Problem 55
Find each product. See Example 5. (5r - 3t²)²
Problem 57
Find each product. See Example 5. (x + 1) (x + 1) (x - 1) (x - 1)