Answer:

To divide the polynomial by the monomial, you can perform the division term by term. Here's how you can do it:

Dividend: 6(x⁴y³z² - x³y⁴z² + x²y²z³)

Divisor: 2xyz

Dividing each term by 2xyz:

(6x⁴y³z²)/(2xyz) - (6x³y⁴z²)/(2xyz) + (6x²y²z³)/(2xyz)

Simplifying each term:

3x³yz - 3x²y³z + 3xy²z²

So, the result of dividing the polynomial by 2xyz is:

3x³yz - 3x²y³z + 3xy²z²

Answer:

3x³y²z - (1/2)xy³z + (1/2)x²y²z.

Step-by-step explanation:

To divide the polynomial 6(x⁴y³z² - x³y⁴z² + x²y²z³) by the monomial 2xyz, we can apply the division property of exponents.

Step 1: Divide the numerical coefficient:

- Divide 6 by 2, which gives us 3.

Step 2: Divide each term in the polynomial by the monomial:

- Divide (x⁴y³z²) by (2xyz). Since both terms have the same variables, we can subtract their exponents: (4-1)x⁴/1y³/1z²/1 = 4x³y²z.

- Divide (-x³y⁴z²) by (2xyz): (-1/2)x³/1y⁴/1z²/1 = (-1/2)xy³z.

- Divide (x²y²z³) by (2xyz): (1/2)x²/1y²/1z³/1 = (1/2)x²y²z.

Therefore, the result of dividing the polynomial 6(x⁴y³z² - x³y⁴z² + x²y²z³) by the monomial 2xyz is:

3x³y²z - (1/2)xy³z + (1/2)x²y²z.

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