Question

what are the possible values of a such that ( a^2 b = 12 ), ( |a| < 20 ), ( |b| < 20 ), and a and b are integers?
a. -1, 1
b. -2, 2
c. -1, 1, -2, 2
d. -1, 1, -3, 3

select the reasoning answer choices that can be eliminated. select all that apply:
-1, 1
-1, 1, -2, 2
-1, 1, -3, 3

Explanation:

Step1: List factor pairs of 12

Integer pairs $(a,b)$ where $a \times b = 12$:
$(1,12), (-1,-12), (2,6), (-2,-6), (3,4), (-3,-4), (4,3), (-4,-3), (6,2), (-6,-2), (12,1), (-12,-1)$

Step2: Filter by $|a|<20, |b|<20$

All pairs satisfy this condition. Extract valid $a$ values: $\pm1, \pm2, \pm3, \pm4, \pm6, \pm12$

Step3: Match to options

Valid $a$ set includes $\pm1, \pm2$. Options missing these full valid values can be eliminated.

• Option A ($-1, 1$) excludes $\pm2$, so it is invalid.
• Option D ($-1, 1, -3, 3$) excludes $\pm2$, so it is invalid.

Answer:

First question: C. $-1, 1, -2, 2$
Second question:

• $-1, 1$
• $-1, 1, -3, 3$