Question

Use long division to divide 3x3−9x2−723x2−2 .(1 point) Responses x−3 x minus 3 x−3+2x−78 x minus 3 plus 2 x minus 78 x−3+2x−723x2−2 x minus 3 plus Start Fraction 2 x minus 72 over 3 x squared minus 2 End Fraction x−3+2x−783x2−2

Answer 1

To use long division to divide \( 3x^3 - 9x^2 - 72 \) by \( x - 3 \), we will follow these steps:

1. **Set up the division**: Write \( 3x^3 - 9x^2 - 72 \) inside the long division symbol and \( x - 3 \) outside.

2. **Divide the leading term**: Divide the leading term of \( 3x^3 \) by the leading term of \( x - 3 \) (which is \( x \)):
\[
\frac{3x^3}{x} = 3x^2
\]

3. **Multiply and subtract**: Multiply \( 3x^2 \) by \( x - 3 \) and subtract from the original polynomial:
\[
3x^2(x - 3) = 3x^3 - 9x^2
\]
Subtract this from \( 3x^3 - 9x^2 \):
\[
(3x^3 - 9x^2) - (3x^3 - 9x^2) = 0
\]
Now we bring down the next term, which is \( -72 \).

4. **Repeat**: Now we divide \( -72 \) by \( x - 3 \):
Since there are no \( x \) terms left to divide, we keep the divisor \( x - 3 \) and write \( -72 \) as \( -72 \div (x - 3) \).

5. **Write the result**: Combine what we have calculated:
\[
3x^2 + \frac{-72}{x - 3}
\]

Thus, the complete division process gives us:
\[
3x^2 - 72/(x - 3)
\]

So the final answer is:
\[
3x^2 - \frac{72}{x - 3}
\]

This indicates the quotient is \( 3x^2 \) with a remainder of \( -72 \). If you need more simplification or a different format, let me know!