A rectangle model forms signed tiles for ((x-5)(x-7)). What is the visual meaning of the middle term?

Correct answer: Total (-12x) from two negative strips

The direct answer is B: the two negative strips together have total area -12x. Expand the product carefully: (x-5)(x-7)=x·x+x(-7)+(-5)x+(-5)(-7)=x^2-7x-5x+35=x^2-12x+35. In a signed tile model, the x by x tile is positive, each strip involving one negative constant is negative, and the corner formed by two negative constants is positive. Thus the strips have signed areas -7x and -5x, and they add to -12x. Option A has the wrong sign because the strip lengths are negative. Option B correctly represents both strips and their sum. Option C confuses the constant corner 35 with a strip and incorrectly writes 35x. Option D would require one positive and one negative strip of equal or opposite contribution; here both strips are negative, so they do not cancel. Memory cue: one negative factor makes a negative strip; two negative factors make a positive corner.