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Simplify 4x^2−12x+24/4x

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

11 answers

To simplify the expression \(\frac{4x^2 - 12x + 24}{4x}\), we first factor out the numerator:

  1. Factor out the common factor of 4 from the numerator: \[ 4x^2 - 12x + 24 = 4(x^2 - 3x + 6). \] So the expression becomes: \[ \frac{4(x^2 - 3x + 6)}{4x}. \]

  2. Now, we can cancel the common factor of 4: \[ = \frac{x^2 - 3x + 6}{x}. \]

  3. Next, we can break this fraction into two parts: \[ = \frac{x^2}{x} - \frac{3x}{x} + \frac{6}{x}. \]

  4. Simplifying each term gives us: \[ = x - 3 + \frac{6}{x}. \]

Thus, the simplified expression in standard form is: \[ x - 3 + \frac{6}{x}. \]

Simplify 15x^5−3x^3+9x^2/3x
. Write your answer in standard form.(1 point)

To simplify the expression \(\frac{15x^5 - 3x^3 + 9x^2}{3x}\), we can follow these steps:

  1. Separate the terms in the numerator: \[ \frac{15x^5}{3x} - \frac{3x^3}{3x} + \frac{9x^2}{3x} \]

  2. Simplify each term:

    • For \(\frac{15x^5}{3x}\): \[ = \frac{15}{3} \cdot \frac{x^5}{x} = 5x^{5-1} = 5x^4 \]
    • For \(\frac{3x^3}{3x}\): \[ = \frac{3}{3} \cdot \frac{x^3}{x} = 1 \cdot x^{3-1} = x^2 \]
    • For \(\frac{9x^2}{3x}\): \[ = \frac{9}{3} \cdot \frac{x^2}{x} = 3 \cdot x^{2-1} = 3x \]

  3. Combine the simplified terms: \[ 5x^4 - x^2 + 3x \]

Now we arrange the expression in standard form, which is typically from the highest degree to the lowest degree:

The final simplified expression is: \[ 5x^4 + 3x - x^2 \]

When arranged in standard form, it is: \[ 5x^4 - x^2 + 3x \]

What is the quotient of 14x^2−21/7
?(1 point)

To find the quotient of \(\frac{14x^2 - 21}{7}\), we can simplify each term in the numerator by dividing by 7:

  1. Separate the terms in the numerator: \[ \frac{14x^2}{7} - \frac{21}{7} \]

  2. Simplify each term:

    • For \(\frac{14x^2}{7}\): \[ = 2x^2 \]
    • For \(\frac{21}{7}\): \[ = 3 \]

  3. Combine the results: \[ 2x^2 - 3 \]

Thus, the final quotient is: \[ 2x^2 - 3 \]

What is the quotient of the following?

68x^8/4x^3


(1 point)

To find the quotient of \(\frac{68x^8}{4x^3}\), we can simplify it by performing the division as follows:

  1. Divide the coefficients: \[ \frac{68}{4} = 17 \]

  2. Apply the quotient rule for exponents: \[ \frac{x^8}{x^3} = x^{8-3} = x^5 \]

  3. Combine the results: \[ 17x^5 \]

Thus, the final quotient is: \[ 17x^5 \]

What is the quotient of the following?

35x^5−20x^4+45x^3/5x^2


(1 point)

To find the quotient of \(\frac{35x^5 - 20x^4 + 45x^3}{5x^2}\), we can simplify it by dividing each term in the numerator by \(5x^2\):

  1. Separate the terms in the numerator: \[ \frac{35x^5}{5x^2} - \frac{20x^4}{5x^2} + \frac{45x^3}{5x^2} \]

  2. Simplify each term:

    • For \(\frac{35x^5}{5x^2}\): \[ = \frac{35}{5} \cdot \frac{x^5}{x^2} = 7x^{5-2} = 7x^3 \]

    • For \(\frac{20x^4}{5x^2}\): \[ = \frac{20}{5} \cdot \frac{x^4}{x^2} = 4x^{4-2} = 4x^2 \]

    • For \(\frac{45x^3}{5x^2}\): \[ = \frac{45}{5} \cdot \frac{x^3}{x^2} = 9x^{3-2} = 9x \]

  3. Combine the results: \[ 7x^3 - 4x^2 + 9x \]

Thus, the final quotient is: \[ 7x^3 - 4x^2 + 9x \]

Incorrect

Divide the monomial into each term of the polynomial in the numerator. Divide the coefficients and subtract the exponents of the variables.

I apologize for any confusion in my previous response; let's carefully go through the process step by step, focusing on dividing the monomial into each term of the polynomial correctly.

We want to simplify:

\[ \frac{35x^5 - 20x^4 + 45x^3}{5x^2} \]

We will divide each term of the polynomial in the numerator by the monomial \(5x^2\).

  1. Divide the first term: \[ \frac{35x^5}{5x^2} = \frac{35}{5} \cdot \frac{x^5}{x^2} = 7x^{5-2} = 7x^3 \]

  2. Divide the second term: \[ \frac{-20x^4}{5x^2} = \frac{-20}{5} \cdot \frac{x^4}{x^2} = -4x^{4-2} = -4x^2 \]

  3. Divide the third term: \[ \frac{45x^3}{5x^2} = \frac{45}{5} \cdot \frac{x^3}{x^2} = 9x^{3-2} = 9x \]

Now, we combine the simplified terms:

\[ 7x^3 - 4x^2 + 9x \]

Thus, the correct final answer for the quotient is:

\[ 7x^3 - 4x^2 + 9x \]

Thank you for your patience, and I hope this clarification helps!