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Simplify 4x2−12x+24/4x

. Write your answer in standard form.(1 point)

1 answer

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:

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