Which visual partition is suitable for changing x²+xy−20y² into a rectangle?

Correct answer: (x+5y) and (x−4y); signed side lengths

Correct answer: C. To factor x²+xy−20y², look for two signed numbers whose product is −20 and whose sum is +1. The numbers are +5 and −4. Thus x²+xy−20y²=(x+5y)(x−4y). A visual tile or rectangle model shows x², +5xy, −4xy, and −20y²; the cross terms combine to +xy. Option A gives a product of −20y² but a middle coefficient of 19, not 1. Option B gives the correct constant product, but its cross terms are −5xy+4xy=−xy, not +xy. Option D gives −20y², but its cross terms are −10xy+2xy=−8xy. Signed tiles are important: a negative factor changes the sign of the corresponding rectangular region.