Certainly! Let's address each part of the question one by one.
### Part (a)
We need to find three more pairs of integers whose product is -18. Given that the product of 2 and -9 is -18, let's find three other such pairs.
By systematically examining pairs of integers and ensuring their product is -18, we find the following pairs:
1. [tex]\((-18, 1)\)[/tex]: When -18 is multiplied by 1, the product is -18.
2. [tex]\((-9, 2)\)[/tex]: When -9 is multiplied by 2, the product is -18.
3. [tex]\((-6, 3)\)[/tex]: When -6 is multiplied by 3, the product is -18.
These pairs were derived by identifying pairs within a specific range of integers and confirming that their product equals -18.
### Part (b)
To determine if there are more pairs of integers whose product is -18, we thoroughly examine all possible pairs within a manageable range. Below are additional pairs that satisfy the condition:
1. [tex]\((-3, 6)\)[/tex]: When -3 is multiplied by 6, the product is -18.
2. [tex]\((-2, 9)\)[/tex]: When -2 is multiplied by 9, the product is -18.
3. [tex]\((-1, 18)\)[/tex]: When -1 is multiplied by 18, the product is -18.
4. [tex]\((1, -18)\)[/tex]: When 1 is multiplied by -18, the product is -18.
5. [tex]\((2, -9)\)[/tex]: When 2 is multiplied by -9, the product is -18.
6. [tex]\((3, -6)\)[/tex]: When 3 is multiplied by -6, the product is -18.
7. [tex]\((6, -3)\)[/tex]: When 6 is multiplied by -3, the product is -18.
8. [tex]\((9, -2)\)[/tex]: When 9 is multiplied by -2, the product is -18.
9. [tex]\((18, -1)\)[/tex]: When 18 is multiplied by -1, the product is -18.
Considering that we've systematically examined the range from -20 to 20 and have identified all pairs that yield a product of -18, we confirm there are indeed more pairs than the three initially mentioned.
Therefore, the initial pairs we found were:
1. [tex]\((-18, 1)\)[/tex]
2. [tex]\((-9, 2)\)[/tex]
3. [tex]\((-6, 3)\)[/tex]
And there are additional pairs as listed above, confirming that multiple pairs of integers exist whose product is -18. By carefully examining these pairs, we can be certain that the list is exhaustive within the given range.
