Answer: To check if (3x + 2) is a factor of a trinomial, we can use long division or synthetic division. However, we can also use the factor theorem, which states that if f(c) = 0 for a polynomial f(x) and a constant c, then (x - c) is a factor of f(x).
In this case, we can use the factor theorem with c = -2/3 to check if (3x + 2) is a factor:
f(-2/3) = 0 if and only if 3(-2/3) + 2 = 0, which is true. Therefore, (3x + 2) is a factor of f(x) if and only if f(-2/3) = 0.
Using this method, we can check each trinomial:
6x² +19x+10: f(-2/3) = 0. Therefore, (3x + 2) is a factor of 6x² +19x+10.
6x²-x-2: f(-2/3) = 0. Therefore, (3x + 2) is a factor of 6x²-x-2.
6x² +7x-3: f(-2/3) ≠ 0. Therefore, (3x + 2) is not a factor of 6x² +7x-3.
6х2 - 5x - 6: f(-2/3) ≠ 0. Therefore, (3x + 2) is not a factor of 6х2 - 5x - 6.
12x²-x-6: f(-2/3) ≠ 0. Therefore, (3x + 2) is not a factor of 12x²-x-6.
Therefore, the trinomials that have (3x + 2) as a factor are:
6x² +19x+10
6x²-x-2
Note: We could also use long division or synthetic division to confirm our results.
Explanation: