Final answer:
The expression 12x³−18x²+9x+3 divided by 3x simplifies to 4x²−6x+3, which is option A.
Step-by-step explanation:
To simplify the expression 12x³−18x²+9x+3 divided by 3x, we can divide each term in the numerator by 3x. Here's how it's done step by step:
- Divide 12x³ by 3x, which gives us 4x².
- Divide −18x² by 3x, which gives us −6x.
- Divide 9x by 3x, which gives us 3.
- The constant term 3 is not divisible by x, so it remains as 3 in the quotient.
Combining all the simplified terms, we get the expression 4x² −6x + 3. Therefore, the simplified expression is 4x² −6x + 3, which corresponds to option A.