What is the quotient of the expression 5x^4 divided by 3x^2 multiplied by 4x and then by 1?

To find the quotient of the expression 5x⁴ divided by (3x² * 4x * 1), we will follow these steps:

1. Multiply the terms in the denominator:
   • We have 3x² * 4x. To multiply these, we multiply the coefficients first: 3 * 4 = 12.
   • Next, we multiply the variable parts: x² * x = x³.
   • So, 3x² * 4x simplifies to 12x³.
2. Since we are also multiplying by 1:
   • Any number multiplied by 1 remains the same. Therefore, the complete denominator remains 12x³.

Now, we can express our original division as:

Quotient = &frac{5x⁴}{12x³}

Step 3: Divide the polynomials:

1. Coefficients:
   • 5 divided by 12 cannot be simplified further, so we will leave it as &frac{5}{12}.
2. Variables:
   • To divide x⁴ by x³, we subtract the powers: 4 – 3 = 1.
   • This means that x⁴ / x³ = x¹ = x.

Putting it all together, the final simplified quotient is:

Quotient = &frac{5}{12} x

So, the final result of the division of 5x⁴ by 3x² * 4x * 1 is:

&frac{5}{12} x