Factor x3 - 7x2 - 5x + 35 by grouping. What is the resulting expression? (x2 - 7) (x - 5) (x2 - 7) (x + 5) (x2 - 5) (x - 7) (x2 + 5) (x - 7)

Factor 15x3 - 5x2 + 6x - 2 by grouping. What is the resulting expression? (5x2 + 2) (3x - 1) (5x2 - 2) (3x + 1) (15x2 + 2) (x - 1) (15x2 - 2) (x + 1)

We can group x³ - 7x² - 5x + 35 into two pairs and look for common factors. x³ - 7x² - 5x + 35 as follows. (x³ - 7x²) + ( - 5x + 35) = x² (x - 7) - 5 (x - 7) If we group the common factor, (x - 7), we'll have (x - 7) (x² - 5). That means the answer is C. Similarly for the second item, 15x³ - 5x² + 6x - 2, we can group the expressions into (15x³ - 5x²) + (6x - 2) = 5x² (3x - 1) + 2 (3x - 1) If we group the common factor, (3x - 1), we'll have (3x - 1) (5x² + 2). Thus, the answer is A.