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In polynomial long division, what is the first step when dividing 4x^3 by 2x?

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Question: In polynomial long division, what is the first step when dividing 4x^3 by 2x?

Options:

  1. Multiply 2x by 2x^2.
  2. Subtract 2x from 4x^3.
  3. Divide 4 by 2.
  4. Add the exponents.

Correct Answer: Multiply 2x by 2x^2.

Solution: 

The first step in polynomial long division is to divide the leading term of the dividend by the leading term of the divisor, which in this case is 4x^3 ÷ 2x = 2x^2.

In polynomial long division, what is the first step when dividing 4x^3 by 2x?

Practice Questions

Q1
In polynomial long division, what is the first step when dividing 4x^3 by 2x?
  1. Multiply 2x by 2x^2.
  2. Subtract 2x from 4x^3.
  3. Divide 4 by 2.
  4. Add the exponents.

Questions & Step-by-Step Solutions

In polynomial long division, what is the first step when dividing 4x^3 by 2x?
  • Step 1: Identify the leading term of the dividend, which is 4x^3.
  • Step 2: Identify the leading term of the divisor, which is 2x.
  • Step 3: Divide the leading term of the dividend (4x^3) by the leading term of the divisor (2x).
  • Step 4: Calculate 4x^3 ÷ 2x, which equals 2x^2.
  • Polynomial Long Division – The process of dividing a polynomial by another polynomial, similar to numerical long division, focusing on the leading terms.
  • Leading Terms – The terms with the highest degree in a polynomial, which are crucial for determining the first step in division.
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