Simplify 4x^2 - 12x + 24/(4x Write your answer in standard form.

Answer 1

To simplify the expression \(\frac{4x^2 - 12x + 24}{4x}\), we can start by dividing each term in the numerator by \(4x\).

1. Express the numerator: \[ 4x^2 - 12x + 24 \]

2. Split the fraction: \[ \frac{4x^2}{4x} - \frac{12x}{4x} + \frac{24}{4x} \]

3. Simplify each term:

   • \(\frac{4x^2}{4x} = x\)
   • \(\frac{12x}{4x} = 3\)
   • \(\frac{24}{4x} = \frac{6}{x}\)

4. Combine the simplified terms: \[ x - 3 + \frac{6}{x} \]

So, the simplified expression is: \[ x - 3 + \frac{6}{x} \]

This is the answer in standard form. If desired, it can also be combined into a single fraction: \[ \frac{x^2 - 3x + 6}{x} \] However, the first version is typically preferred for simplicity.

Answer 2

thats wrong

Answer 3

Let's carefully go through the simplification of the expression \(\frac{4x^2 - 12x + 24}{4x}\) step by step again.

1. Start with the expression: \[ \frac{4x^2 - 12x + 24}{4x} \]

2. Factor out the common factor in the numerator: The numerator \(4x^2 - 12x + 24\) can be factored: \[ 4(x^2 - 3x + 6) \]

3. Rewrite the expression: \[ \frac{4(x^2 - 3x + 6)}{4x} \]

4. Cancel the common factor of 4: \[ = \frac{x^2 - 3x + 6}{x} \]

5. Split the terms: Now we can express this as: \[ = \frac{x^2}{x} - \frac{3x}{x} + \frac{6}{x} \] Which simplifies to: \[ = x - 3 + \frac{6}{x} \]

Thus, the final simplified form of \( \frac{4x^2 - 12x + 24}{4x} \) is: \[ \boxed{x - 3 + \frac{6}{x}} \]

If I made an error in understanding your question, please let me know!

Answer 4

Simplify 15x^5 - 3x^3 + 9x^2/3x Write your answer in standard form.

Answer 5

To simplify the expression \(\frac{15x^5 - 3x^3 + 9x^2}{3x}\), we will divide each term in the numerator by \(3x\).

1. Start with the expression: \[ \frac{15x^5 - 3x^3 + 9x^2}{3x} \]

2. Split the fraction into separate terms: \[ \frac{15x^5}{3x} - \frac{3x^3}{3x} + \frac{9x^2}{3x} \]

3. Simplify each term:

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

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

5. Write in standard form (which is in descending order of exponents): \[ 5x^4 + 3x - x^2 \]

   Rearranging gives us: \[ 5x^4 - x^2 + 3x \]

Thus, the final simplified expression in standard form is: \[ \boxed{5x^4 - x^2 + 3x} \]

Answer 6

What is the quotient of 14x^2 - 21/7?

Answer 7

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

1. Start with the expression: \[ \frac{14x^2 - 21}{7} \]

2. Split the fraction into separate terms: \[ \frac{14x^2}{7} - \frac{21}{7} \]

3. Simplify each term:

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

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

Therefore, the quotient of \(\frac{14x^2 - 21}{7}\) is: \[ \boxed{2x^2 - 3} \]

Answer 8

What is the quotient of the following?
68x^8/4x^3

Answer 9

To find the quotient of \( \frac{68x^8}{4x^3} \), we divide the coefficients and subtract the exponents of \( x \).

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

2. Subtract the exponents of \( x \): \[ x^{8-3} = x^5 \]

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

Therefore, the quotient of \( \frac{68x^8}{4x^3} \) is: \[ \boxed{17x^5} \]

Answer 10

What is the quotient of the following?
(35x^5 - 20x^4 + 45x^3)/(5x^2)

Answer 11

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

1. Start with the expression: \[ \frac{35x^5 - 20x^4 + 45x^3}{5x^2} \]

2. Split the fraction into separate terms: \[ \frac{35x^5}{5x^2} - \frac{20x^4}{5x^2} + \frac{45x^3}{5x^2} \]

3. Simplify each term:

   • For \(\frac{35x^5}{5x^2}\): \[ = \frac{35}{5} x^{5-2} = 7x^3 \]
   • For \(\frac{20x^4}{5x^2}\): \[ = \frac{20}{5} x^{4-2} = 4x^2 \]
   • For \(\frac{45x^3}{5x^2}\): \[ = \frac{45}{5} x^{3-2} = 9x \]

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

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