Question

Simplify 4x2−12x+24/4x
. Write your answer in standard form.(1 point)

Answer 1

To simplify the expression \(\frac{4x^2 - 12x + 24}{4x}\), we can follow these steps:

1. **Factor the numerator**:
The numerator is \(4x^2 - 12x + 24\). We can factor out a 4:

\[
4(x^2 - 3x + 6)
\]

2. **Rewrite the expression**:
Now, substitute the factored numerator into the original expression:

\[
\frac{4(x^2 - 3x + 6)}{4x}
\]

The 4's in the numerator and denominator cancel out:

\[
\frac{x^2 - 3x + 6}{x}
\]

3. **Separate the expression**:
Now, we can split the single fraction into separate terms:

\[
\frac{x^2}{x} - \frac{3x}{x} + \frac{6}{x}
\]

This simplifies to:

\[
x - 3 + \frac{6}{x}
\]

4. **Write in standard form**:
The standard form of a polynomial or expression typically lists terms in descending order:

\[
x - 3 + \frac{6}{x}
\]

Therefore, the final simplified expression is:

\[
x - 3 + \frac{6}{x}
\]