Question

Prove |(b+c,a,a²) (c+a,b,b²) (a+b,c,c²)| = (a+b+c) (a-b) (b-c) (c-a) , using factor theorem​

Answer 1

Answer:

We know that the factor theorem states that if the polynomial p(x) is divided by (cx−d) and the remainder, given by p(cd), is equal to zero, then (cx−d) is a factor of p(x).

Consider the given expression a(b2−c2)+b(c2−a2)+c(a2−b2) and solving it as follows:

a(b2−c2)+b(c2−a2)+c(a2−b2)=ab2−ac2+bc2−ba2+c(a−b)(a+b)(∵(x+y)(x−y)=x2−y2)=ab2−ba2−ac2+bc2+c(a−b)(a+b)=ab(b−a)−(a−b)c2+c(a−b)(a+b)=−ab(a−b)−(a−b)c2+c(a−b)(a