1. The problem is to analyze the given sets of polynomial expressions and understand their relationships or properties. 2. Let's examine each set: - Set 1: $x - 3$, $x + 1$, $4x - 2$ - Set 2: $3x$, $x - 7$, $x + 7$ - Set 3: $4$, $x$, $x^2 - 1$ - Set 4: $x + 2$, $x + 4$, $2x + 11$ 3. We can check if any of these sets form arithmetic sequences, geometric sequences, or have other notable algebraic properties. 4. For example, in Set 1, check if the difference between consecutive terms is constant: $$ (x + 1) - (x - 3) = 4 $$ $$ (4x - 2) - (x + 1) = 3x - 3 $$ Since $4 \neq 3x - 3$, Set 1 is not an arithmetic sequence. 5. Similarly, check Set 2 differences: $$ (x - 7) - 3x = -2x - 7 $$ $$ (x + 7) - (x - 7) = 14 $$ Not constant, so not arithmetic. 6. Set 3 has constants and polynomials of different degrees, so no arithmetic or geometric sequence. 7. Set 4 differences: $$ (x + 4) - (x + 2) = 2 $$ $$ (2x + 11) - (x + 4) = x + 7 $$ Not constant, so not arithmetic. 8. Without further instructions, the problem is to identify these properties. Final answer: None of the given sets form arithmetic sequences based on the differences between consecutive terms.