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What is the coefficient of x^0 in the expansion of (3x - 4)^5?

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Question: What is the coefficient of x^0 in the expansion of (3x - 4)^5?

Options:

  1. -1024
  2. 243
  3. -243
  4. 1024

Correct Answer: -1024

Solution: 

The coefficient of x^0 is (-4)^5 = -1024.

What is the coefficient of x^0 in the expansion of (3x - 4)^5?

Practice Questions

Q1
What is the coefficient of x^0 in the expansion of (3x - 4)^5?
  1. -1024
  2. 243
  3. -243
  4. 1024

Questions & Step-by-Step Solutions

What is the coefficient of x^0 in the expansion of (3x - 4)^5?
Correct Answer: -1024
  • Step 1: Understand that x^0 means we are looking for the constant term in the expansion.
  • Step 2: Use the Binomial Theorem, which states that (a + b)^n = sum of (n choose k) * a^(n-k) * b^k for k = 0 to n.
  • Step 3: In our case, a = 3x, b = -4, and n = 5.
  • Step 4: The constant term occurs when the power of x is 0, which happens when we choose all of b (-4) and none of a (3x).
  • Step 5: This means we need to calculate (-4)^5.
  • Step 6: Calculate (-4)^5 = -1024.
  • Step 7: Therefore, the coefficient of x^0 is -1024.
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