Advanced Math practice question

Answer: A. 2x − 5

4x² − 25 = (2x)² − 5², a difference of squares: (2x − 5)(2x + 5). So 2x − 5 is a factor. (Check: x = 5/2 makes 4x² − 25 zero.)

Why the other answers are wrong

B. 4x − 5

4x − 5 would need 4x² − 25 to be zero at x = 5/4, but it is −75/4 there.

C. x − 5

x − 5 is a factor of x² − 25, not of 4x² − 25 (which is 75 at x = 5).

D. 2x + 25

2x + 25 would need a zero at x = −25/2; the expression is 600 there.

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