A rectangle model represents the quadratic expression x² + 11x + 30 in four parts. What could its two side lengths be?

Correct answer: (x + 5) and (x + 6)

The correct answer is C, (x + 5) and (x + 6). To find the rectangle’s sides, factor the expression by looking for two numbers whose product is 30 and whose sum is 11. The numbers 5 and 6 satisfy both conditions: 5 × 6 = 30 and 5 + 6 = 11. Therefore, x² + 11x + 30 = (x + 5)(x + 6). In a visual model, x² is the large square, 5x and 6x are the two rectangular strips, and 30 is the small corner rectangle. Option A gives 3 × 8 = 24 and 3 + 8 = 11, so its constant term is wrong. Option B gives 25, not 30. Option C satisfies both product and sum. Option D gives 30 as the product but 17 as the sum, so its middle term is wrong. Memory cue: for x² + bx + c, check both sum = b and product = c.