Question

Simplify: start fraction, minus, 3, x, to the power 4 , minus, 3, x, cubed, minus, 9, x, squared, divided by, 3, x, squared, end fraction
3x
2

−3x
4
−3x
3
−9x
2

​

Answer
Attempt 1 out of 2

Answer 1

To simplify the expression

\[
\frac{-3x^4 - 3x^3 - 9x^2}{3x^2}
\]

we can start by factoring out the common terms in the numerator.

1. **Factor out -3 from the numerator**:

\[
-3(x^4 + x^3 + 3x^2)
\]

Now the expression becomes:

\[
\frac{-3(x^4 + x^3 + 3x^2)}{3x^2}
\]

2. **Cancel the common term (-3)**:

\[
\frac{-3}{3} \cdot \frac{x^4 + x^3 + 3x^2}{x^2} = -1 \cdot \frac{x^4 + x^3 + 3x^2}{x^2}
\]

3. **Divide each term in the numerator by \(x^2\)**:

\[
- (x^4/x^2 + x^3/x^2 + 3x^2/x^2) = - (x^2 + x + 3)
\]

4. **Final simplified expression**:

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

Thus, the simplified form of the original expression is:

\[
-x^2 - x - 3
\]