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When asked to factor the trinomial 𝑥2−16𝑥+64x 2 −16x+64, a student gives the answer (x – 8)(x + 8). Which of the following statements is true?A.The answer is incorrect; the trinomial cannot be factored.B.The answer is incorrect; the minus sign should be a plus sign.C.The answer is correct.D.The answer is incorrect; the plus sign should be a minus sign.

Question

When asked to factor the trinomial 𝑥2−16𝑥+64x 2 −16x+64, a student gives the answer (x – 8)(x + 8). Which of the following statements is true?A.The answer is incorrect; the trinomial cannot be factored.B.The answer is incorrect; the minus sign should be a plus sign.C.The answer is correct.D.The answer is incorrect; the plus sign should be a minus sign.

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Solution

B. The answer is incorrect; the minus sign should be a plus sign.

Here's why:

The trinomial x^2 - 16x + 64 can be factored as (x - 8)(x - 8) or (x - 8)^2, not (x - 8)(x + 8).

The student seems to have confused this with the difference of squares factoring rule, which states that a^2 - b^2 = (a - b)(a + b). However, this rule doesn't apply here because we have a positive 64 (the square of 8), not a negative one.

This problem has been solved

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