Okay, let's solve this step by step.
We know the dividend is 6x²-27x+16, the quotient is 6x-3 and the remainder is 4. We need to find the divisor (let's call it b).
Remember the important relationship in polynomial division: dividend = divisor * quotient + remainder.
Let's express the dividend in terms of b (divisor), q (quotient) and r (remainder). As per the equation above, we can write it as:
6x²-27x+16 = b * (6x-3) + 4
To isolate b and get it on one side of the equation, we rearrange to:
b = (6x²-27x+16 - 4) / (6x-3)
Plugging in the values for x, q and r, we get:
b = (6x²-27x+12) / (6x-3)
So, the divisor or polynomial 'b' that we need to find is (6x²-27x+12) / (6x-3).
Therefore, when the polynomial 6x²-27x+16 is divided by (6x²-27x+12) / (6x-3), we get a quotient of 6x-3 and a remainder of 4.
And that concludes the solution to your problem. If you have any questions or require further clarification, feel free to ask.