1. An instructor writes four expressions on the board and asks students to rank them by the value of their leading coefficient $a$, from smallest to largest: (I) $-2x^2 + x$, (II) $5 - x + \frac{3}{4}x^2$, (III) $x^2 - 1$, (IV) $4x^2$. What is the correct ranking?
- A.IV, III, II, I
- B.I, II, III, IV
- C.II, I, III, IV
- D.I, III, II, IV
View Answer
Answer: I, II, III, IV
Find each leading coefficient: (I) $a = -2$. (II) Rewritten in standard form: $\frac{3}{4}x^2 - x + 5$, so $a = \frac{3}{4} = 0.75$. (III) $a = 1$. (IV) $a = 4$. Sort from smallest to largest: $-2 < 0.75 < 1 < 4$, so the order is I, II, III, IV. Why distractors fail: Option A reverses the order. Option C swaps I and II. Option D places III before II, but $0.75 < 1$.