Answer:
10. (-1, 7), (-7, 1)
11. (8, 4), (16, 2)
Step-by-step explanation:
10.
Let x and y represent the two missing factors. Then you have ...
-3xy = 21
xy = -7 . . . . . . . divide by -3
Integer divisors of -7 are ±1, ±7, so possible factor pairs are (-1, 7), (-7, 1) and their reverse.
Of course, the only requirement is that the values be rational, so we could have (-1/4, 28), for example. One of the above factors can be multiplied by any rational number, and the other multiplied by its inverse.
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11.
If the two factors of interest are x and y, then the product of the three factors is ...
(-3/4)xy = -24
xy = (-4/3)(-24) = 32
Integer divisors of 32 are 1, 2, 4, 8, 16, 32. So, any of those, positive or negative, could be one of the (integer) factors you're looking for. On the attached graph, we have shown (x, y) pairs ...
(8, 4), (16, 2), (-4, -8)
There are an infinite number of possibilities.
