Question

use the long division method to find the result when 3x^3+17x^2+30x+18 is divided by x+3

please dont get another wrong answer

Answer 1

To divide \(3x^3 + 17x^2 + 30x + 18\) by \(x + 3\) using long division, we can follow these steps:

1. **Set up the division**: Write \(3x^3 + 17x^2 + 30x + 18\) under the long division symbol and \(x + 3\) outside.

\[
\begin{array}{r|l}
x + 3 & 3x^3 + 17x^2 + 30x + 18 \\
\end{array}
\]

2. **Divide the first term**: Divide the leading term \(3x^3\) by the leading term of \(x + 3\) (which is \(x\)). This gives:

\[
\frac{3x^3}{x} = 3x^2
\]

3. **Multiply**: Multiply \(3x^2\) by \(x + 3\):

\[
3x^2(x + 3) = 3x^3 + 9x^2
\]

4. **Subtract**: Subtract this result from the original polynomial:

\[
(3x^3 + 17x^2 + 30x + 18) - (3x^3 + 9x^2) = (17x^2 - 9x^2) + 30x + 18 = 8x^2 + 30x + 18
\]

5. **Bring down the next term**: In this case, since we are already down to the next set of terms, we can proceed to the next step.

6. **Divide again**: Now divide the leading term \(8x^2\) by \(x\):

\[
\frac{8x^2}{x} = 8x
\]

7. **Multiply**: Multiply \(8x\) by \(x + 3\):

\[
8x(x + 3) = 8x^2 + 24x
\]

8. **Subtract**: Subtract this from \(8x^2 + 30x + 18\):

\[
(8x^2 + 30x + 18) - (8x^2 + 24x) = (30x - 24x) + 18 = 6x + 18
\]

9. **Divide the next term**: Now divide the leading term \(6x\) by \(x\):

\[
\frac{6x}{x} = 6
\]

10. **Multiply**: Multiply \(6\) by \(x + 3\):

\[
6(x + 3) = 6x + 18
\]

11. **Subtract**: Subtract this from \(6x + 18\):

\[
(6x + 18) - (6x + 18) = 0
\]

Now that we have zero, there are no more terms to bring down.

So the final result of the division is:

\[
3x^2 + 8x + 6
\]

Thus,

\[
\frac{3x^3 + 17x^2 + 30x + 18}{x + 3} = 3x^2 + 8x + 6
\]

And the remainder is \(0\).