Could you help me with this long division problem of a polynomial?

18x4+9x3+3x2/3x2+1

I'm not sure, but my answer would be 15. you multiply 18x4=72, 9x3=27, 3x2=6 add them together, it makes 105 divided by 3x2+1=7, so 105 divided by 7=15.

I hope it helps

Of course! I can guide you through the process of solving the long division problem for these polynomials.

Step 1: Write the division problem in the proper format.
The dividend is 18x^4 + 9x^3 + 3x^2, and the divisor is 3x^2 + 1.

Step 2: Divide the first term of the dividend by the first term of the divisor.
The first term of the dividend is 18x^4, and the first term of the divisor is 3x^2. Divide 18x^4 by 3x^2, which gives us 6x^2.

Step 3: Multiply the result from Step 2 by the divisor.
Multiply 6x^2 by both terms of the divisor: 6x^2 * (3x^2 + 1) = 18x^4 + 6x^2.

Step 4: Subtract the product obtained in Step 3 from the dividend.
Subtract 18x^4 + 6x^2 from the dividend 18x^4 + 9x^3 + 3x^2: (18x^4 + 9x^3 + 3x^2) - (18x^4 + 6x^2) = 9x^3 - 3x^2.

Step 5: Bring down the next term from the dividend.
The next term in the dividend is 0x (which represents nothing), so we move on to the next step.

Step 6: Divide the term obtained in Step 5 by the first term of the divisor.
The term obtained in Step 5 is -3x^2, and the first term of the divisor is 3x^2. Divide -3x^2 by 3x^2, which gives us -1.

Step 7: Multiply the result from Step 6 by the divisor.
Multiply -1 by both terms of the divisor: -1 * (3x^2 + 1) = -3x^2 - 1.

Step 8: Subtract the product obtained in Step 7 from the result of Step 4.
Subtract -3x^2 - 1 from the term obtained in Step 4: (9x^3 - 3x^2) - (-3x^2 - 1) = 9x^3 - 3x^2 + 3x^2 + 1 = 9x^3 + 1.

Step 9: We have obtained the quotient and there are no more terms in the dividend, so we have the final result.
The final result of the long division is 6x^2 - 1 as the quotient and the remainder is 9x^3 + 1.

Therefore, the answer to the division problem is:
Quotient: 6x^2 - 1
Remainder: 9x^3 + 1