Consider the polynomial (x-a)(x-b) and the real number line is shown below. For each of the three subintervals of the real number line, write the sign of each factor and the sign of the product.

Question

Consider the polynomial (x-a)(x-b). For each of the three subintervals of the real number line, write the sign of each factor and the sign of the product.

Answer 1

for x<a, (x-a) <0, (x-b) <0 and (x-a)(x-b) >0

for a<x<b (x-a)>0, (x-b)<0 and (x-a)(x-b) <0

for x> b (x-a)>0, (x-b)>0 and (x-a)(x-b) >0