Advanced Math practice question

Answer: A. (x − 5)²

Look for two numbers with product 25 and sum −10: −5 and −5. So x² − 10x + 25 = (x − 5)(x − 5) = (x − 5)². Check: (x − 5)² = x² − 10x + 25.

Why the other answers are wrong

B. (x + 5)²

(x + 5)² expands to x² + 10x + 25; the middle term has the wrong sign.

C. (x − 5)(x + 5)

(x − 5)(x + 5) = x² − 25, with no middle term at all.

D. (x − 25)(x + 1)

(x − 25)(x + 1) = x² − 24x − 25: wrong middle term and wrong constant.

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