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Use the long division method to find the result when [tex]4x^4[/tex] is divided by [tex]3x - 2[/tex].

Dividend: [tex]4x^4 + 9x^3 + 9x^2 - 4x[/tex]

Answer :

Final answer:

To divide the expression 4x^4 by 3x - 2 using the long division method, follow the steps and obtain the result 9x³ + 9x² - 4x.


Explanation:

To divide the expression 4x4 by 3x - 2 using the long division method, we proceed as follows:

  1. First, divide the first term of the dividend by the first term of the divisor. In this case, (4x4) / (3x) = (4/3)x3.
  2. Multiply the divisor by the quotient obtained in step 1, and subtract the product from the dividend. Thus, 4x4 - (4/3)x(3x - 2) = 11x3 + 8x.
  3. Repeat the process with the new dividend obtained in step 2.
  4. Continue until we cannot perform the division anymore.

The final result of dividing 4x4 by 3x - 2 is: 9x³ + 9x² - 4x.


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