ISEE Word Problems Question 239: Answer and Explanation

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Question: 239

3. If k is a positive integer, and (x + 11)2 = x2 + kx + 121, what is the value of k ?

  • A. 121
  • B. 55
  • C. 22
  • D. 11

Correct Answer: C

Explanation:

The answer is C

Use FOIL (First, Outside, Inside, Last) on the two factors: (x + 11)(x + 11) = (x2 + 11x + 11x + 121). Combine like terms: x2 + 22x + 121. Thus, k = 22.

Plug in a number for x, such as 2, and solve both sides of the equation: 132 = 4 + 2k + 121, 169 = 125 + 2k. Combine like terms and divide by 2: k = 22.

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