Final answer:
Upon simplifying the expression (3x^2 + 7x - 6) / (x + 3), we found that it simplifies to 3(x - 2)/(x + 3), which does not match any of the given options. There could be a mistake in the options provided or the interpretation of the initial expression.
Step-by-step explanation:
To find the simplified form of the expression A = 3x2 + 7x - 6 divided by (x + 3), we must perform polynomial division or factor the numerator, if possible, and then divide by the denominator.
First, let's see if factoring is possible. We need to find two numbers that when multiplied give us 3 × (-6) = -18 and when added give us 7 (the coefficient of x). These two numbers are 9 and -2. Thus, we can rewrite the expression as follows:
A = (3x + 9)(x - 2) divided by (x + 3).
Now we see that (3x + 9) is equivalent to 3 × (x + 3). This allows us to cancel out the (x + 3) terms from the numerator and denominator, leaving us with:
A = (3)(x - 2) divided by (x + 3), which simplifies further to:
A = (3x - 6) divided by (x + 3).
However, this expression does not exactly match any of the provided options. By inspecting the simplified form, we notice that if we were to factor out a 3 from (3x-6), we would get 3(x - 2), which upon division by (x + 3) gives us 3(x - 2)/(x + 3). None of the options matches this result, which suggests there may have been a mistake in the provided options or in the interpretation of the original expression.