Question

for the polynomial a^2(b-c) + b^2(c-a) + c^2(a-b), prove that (a-b) is a factor of it, using factors theorem

Answer 1

Answer:

Step-by-step explanation:

let f(a)=a^2(b-c) + b^2(c-a) + c^2(a-b)

putting a=b mean we will write b in place of b

f(b)=b^2(b-c)+b^2(c-b)+c^2(b-b)

=b^2(b-c+c-b)+c^2*0

=b^2*0+0

=0

so f(b)=0

hence a-b is factor of f(a)

or a-b is factor of the polynomial given