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If the polynomial P(x) = x^3 - 6x^2 + 11x - 6 has a root at x = 1, what is P(2)?

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Question: If the polynomial P(x) = x^3 - 6x^2 + 11x - 6 has a root at x = 1, what is P(2)?

Options:

  1. 0
  2. 1
  3. 2
  4. 3

Correct Answer: 3

Solution: 

P(2) = 2^3 - 6(2^2) + 11(2) - 6 = 8 - 24 + 22 - 6 = 0.

If the polynomial P(x) = x^3 - 6x^2 + 11x - 6 has a root at x = 1, what is P(2)?

Practice Questions

Q1
If the polynomial P(x) = x^3 - 6x^2 + 11x - 6 has a root at x = 1, what is P(2)?
  1. 0
  2. 1
  3. 2
  4. 3

Questions & Step-by-Step Solutions

If the polynomial P(x) = x^3 - 6x^2 + 11x - 6 has a root at x = 1, what is P(2)?
  • Step 1: Identify the polynomial P(x) = x^3 - 6x^2 + 11x - 6.
  • Step 2: Substitute x = 2 into the polynomial to find P(2).
  • Step 3: Calculate 2^3, which is 8.
  • Step 4: Calculate 6(2^2), which is 6 * 4 = 24.
  • Step 5: Calculate 11(2), which is 22.
  • Step 6: Now, combine all the results: P(2) = 8 - 24 + 22 - 6.
  • Step 7: First, do 8 - 24, which equals -16.
  • Step 8: Next, add 22 to -16, which equals 6.
  • Step 9: Finally, subtract 6 from 6, which equals 0.
  • Step 10: Therefore, P(2) = 0.
  • Polynomial Evaluation – The question tests the ability to evaluate a polynomial function at a specific value.
  • Root of a Polynomial – Understanding that a root of a polynomial indicates a value where the polynomial equals zero.
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