When 4x² +3x +1 is divided by x+3,

To divide the polynomial 4x² +3x +1 by x+3, we use polynomial division. Here are the steps:

1. Divide the first term of the numerator (4x²) by the first term of the denominator (x). This gives us 4x. This is the first term of the quotient.

2. Multiply the entire denominator (x+3) by the first term of the quotient (4x). This gives us 4x² + 12x.

3. Subtract this result from the original numerator. This gives us -9x + 1.

4. Repeat the process with the new numerator (-9x + 1). Divide the first term of the new numerator (-9x) by the first term of the denominator (x). This gives us -9. This is the second term of the quotient.

5. Multiply the entire denominator (x+3) by the second term of the quotient (-9). This gives us -9x - 27.

6. Subtract this result from the new numerator (-9x + 1). This gives us 28.

Since 28 cannot be divided by x+3, it is the remainder.

So, when 4x² +3x +1 is divided by x+3, the quotient is 4x - 9 and the remainder is 28. The result can be written as 4x - 9 + 28/(x+3).